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Topic: Lefschetz class

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	Lefschetz biography
		Lefschetz received his Ph.D. in mathematics in 1911 with a thesis on algebraic geometry entitled On the existence of loci with given singularities.
		That same year, 1911, Lefschetz was appointed an instructor in mathematics at the University of Nebraska in Lincoln, then, two years later, he was appointed to the University of Kansas in Lawrence.
		Lefschetz worked on results which provided a deep generalisation of Emile Picard's theorems in function theory to several complex variables.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Lefschetz.html (2111 words)

	Abstracts of my papers
		We also exhibit an automorphism of a subgroup of finite index in the mapping class group of a sphere with four punctures (or a torus) such that it is not the restriction of an endomorphism of the whole group.
		As an application, we prove that a homomorphism from the mapping class group of a nonorientable surface of genus at least nine to the group of real-analytic diffeomorphisms of the circle is either trivial or of order two.
		Using his result, we show that the mapping class group of a sphere with punctures and that the hyperelliptis mapping class groups are linear.
	www.math.metu.edu.tr /~korkmaz/abstracts.html (1508 words)

	The Princeton Mathematics Community in the 1930s (PMC21) (Site not responding. Last check: 2007-11-02)
		At the end of the class he presented us with a complete set of notes for that lecture, written clearly in a precise hand, in ink, and in French.
		Lefschetz had told us that the prelims were the only important exam we would have, and the courses that were offered, except for Bochner's, were not helping me make any progress toward learning what was needed for prelims.
		This was one of the things that Lefschetz had left out of his orientation talk at the beginning of the year.
	libweb.princeton.edu /libraries/firestone/rbsc/finding_aids/mathoral/pmc21.htm (2058 words)

	Introduction to Differentiable Manifolds Home Page (Site not responding. Last check: 2007-11-02)
		Differentiable manifolds are an enrichment of topological manifolds by adding a smooth structure, e.g., a notion of which curves are smooth.
		Since this is not an elementary course, I may assign problems on the homework that develop essential material that is awkward to cover in class.
		The in-class presentations will be from Tuesday, April 30th to Tuesday, May 7th.
	www.math.columbia.edu /~zare/introdm.html (1036 words)

	Algebraic Methods Seminar 2001-02 (Site not responding. Last check: 2007-11-02)
		In a spectacular use of algebraic geometry in combinatorics Stanley completed the proof of McMullen's conjecture which characterizes the possible face vectors (whose entries are the number of faces of the polytope in a given dimension) of a convex simplical polytope.
		An important class of simplical complexes are the so-called matroid complexes.
		For this class we have the still unsettled conjecture of Stanley claiming that the face vector of a matroid complex could be read off from a simple algebraic structure: a pure order ideal.
	math.stanford.edu /hausel.html (266 words)

	The Princeton Mathematics Community in the 1930s (PMC14)
		I think although he was a little taken aback, that little exchange between us really was an entree into a lasting and solidly friendly relation between the two of us.
		Lefschetz was supposed to have been on a trip somewhere, accompanied by a young mathematician.
		I remember very well that it was Lefschetz who sent me over there to do it.
	infoshare1.princeton.edu /libraries/firestone/rbsc/finding_aids/mathoral/pmc14.htm (18319 words)

	Salomon Bochner Lectures, 2004-2005 (Site not responding. Last check: 2007-11-02)
		This series of lectures will aim to provide an overview of a relatively recent set of techniques which can be used to study the topology of symplectic manifolds (a class of smooth manifolds which naturally generalizes the better understood case of smooth projective varieties and plays a central role in mathematical physics).
		In the first lecture, we will introduce symplectic manifolds, and show how they can be described by Lefschetz fibrations (i.e., fibrations over the 2-sphere with isolated nodal singular fibers), focusing particularly on the four-dimensional case.
		We will then discuss how the classification of Lefschetz fibrations reduces to that of "factorizations" in the mapping class group of an oriented surface, and give some partial classification results.
	math.rice.edu /Calendar/bochner06.html (468 words)

	Math 215a Home Page
		Since there are approximately fifty students in the class, it is not possible for me to read all of the homework carefully, and unfortunately I was not able to get a grader.
		If you can't make it to class on the day that the homework is due, please slide your homework under my office door before class, together with a note explaining how I can give you another assignment to grade.
		Application: the Lefschetz fixed point theorem on a smooth manifold (which actually counts fixed points with signs, rather than merely proving that a fixed point exists).
	math.berkeley.edu /~hutching/teach/215a-2005/index.html (2991 words)

	Search Results for Topology
		Solomon Lefschetz was a Russian born, Jewish mathematician who was the main source of the algebraic aspects of topology.
		By topology we mean the doctrine of the modal features of objects, or of the laws of connection, of relative position and of succession of points, lines, surfaces, bodies and their parts, or aggregates in space, always without regard to matters of measure or quantity.
		Tukey's research was supervised by Lefschetz and he received his doctorate in 1939 for a dissertation Denumerability in topology which was published in 1940 as Convergence and uniformity in topology.
	www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=Topology&CONTEXT=1 (14972 words)

	Publications (Lefschetz Center @ Brown University) (Site not responding. Last check: 2007-11-02)
		We study dynamical phenomena for a class of lattice differential equations, namely infinite systems of ordinary differential equations coordinatized by points on a spatial lattice.
		The phenomenon of crystallographic pinning occurs when there is a tendency for a wave to become pinned in selected directions.
		In the present work we show how this phenomenon holds for a general class of systems with smooth nonlinearities and how it follows from general principles of dynamical systems.
	www.dam.brown.edu /lcds/publications/abstract.php?id=2001-011 (138 words)

	Publications (Lefschetz Center @ Brown University) (Site not responding. Last check: 2007-11-02)
		As this paper demonstrates, and in sharp contrast to the great majority of large deviation problems for processes with state dependence, for allocation problems one can construct more-or-less explicit solutions.
		The first class considers objects of a single type with a parameterized family of placement probabilities.
		The second class considers only equally likely placement probabilities, but allows for more than one type of object.
	www.dam.brown.edu /lcds/publications/abstract.php?id=2006-006 (164 words)

	[No title]
		Z is the ring homomorphism sending the class of a finite set S to S which is just the component belonging to the trivial subgro* *up of the character map defined in (1.2).
		The relation of the universal equivariant Euler characteristic to the equi- variant Euler class which is by definition the class of the Euler operator on a cocompact proper smooth G-manifold with G-invariant Riemannian metric in equivariant K-homology defined by Kasparov is analyzed in [31].
		Equivariant Lefschetz classes for G-maps of finite proper G-CW -complexes are studied in [32].
	hopf.math.purdue.edu /Lueck/lueck_burnside0504.txt (10461 words)

	CEU, Department of Mathematics and its Applications (Site not responding. Last check: 2007-11-02)
		Extra bonus points may be earned by presentations as well as by participation in class discussions.
		Tests: Grades are given based on the students' presentations as well as by participation in class discussions.
		Extra bonus points may be earned by presentations and active participation in class discussions.
	www.ceu.hu /math/Courses/wint0405.html (2260 words)

	SVIBOR - Papers quoted in CC - project code: 1-01-253
		This class includes all comapct metric spaces where a similar intrinsic description of the shape category using multi-valued functions was given by Jose M. Sanjurjo.
		We show that for suitable choices of classes A, B, and C these results provide interesting consequences in dimension theory, general topology, shape theory, and in the study of spaces which are like a given class of spaces.
		We also study classes of G-spaces on which equivariant shape and equivariant homotopy coincide, look for conditions under which a G-map f between G-spaces X and Y is an equivariant shape equivalence, and give some characterizations of G-spaces with trivial equivariant shape.
	www.mzos.hr /svibor/1/01/253/rad_cc_e.htm (2747 words)

	The Princeton Mathematics Community in the 1930s [before, during and after]: Related Documents (Site not responding. Last check: 2007-11-02)
		In the 1930s, a remarkable mathematical community was born in a building built specifically to house such an unusual community: Fine Hall at Princeton University (now Jones Hall, reverting to the donors' names with the construction of the new Fine Hall and Jadwin Physics complex in 1970).
		The Mathematics Department of Princeton University, then emerging as a world class center for mathematics, shared its new quarters with the Department of Mathematics of the Institute for Advanced Study for six years while the latter's facilities (Fuld Hall) were planned and constructed nearby.
		Finally as a fundraiser he made an important connection that upon his accidental death in 1928 lead to the donation of funds to build a luxurious new mathematics building to facilitate research, completed in 1931 and dedicated in his honor as Fine Hall.
	libweb.princeton.edu /libraries/firestone/rbsc/finding_aids/mathoral/pm06.htm (2517 words)

	Courses
		An introduction to (abelian) Hecke L-functions and their arithmetic applications to topics such as the distribution of primes and the study of ideal class groups.
		Topics include: spectral sequences and their applications, topology of Lie Groups, H-spaces, Hopf Algebras, homotopy classification of bundles, the Steenrod Algebra and its applications, introduction to generalized cohomology theories, spectra, elements of K-theory.
		Theory of local fields; local and global class field theory; complex multiplication, adeles, ideles, idele class characters, Tchebotarev's Density Theorem, CM elliptic curves, construction of class fields of imaginary quadratic fields.
	www.wisc.edu /grad/catalog/letsci/mathemC.html (3682 words)

	[No title]
		As an "A" class, ours was purely Catholic and Polish, only "B" classes had Jewish and Ukrainian students or those of other religious denominations.
		I never noticed in our class anyone having reservations about the new teacher because of his Jewish extraction, although relations between nationalities and faiths in Poland and in Lwów were not, in general, always the best.
		This type of 8th-grade gymnasium system was just then in liquidation; my class was the last of this system, while my younger brothers were already attending the new school system, without Greek but with more mathematics and physics.
	www-users.mat.uni.torun.pl /~tmna/htmls/mem1.html (5070 words)

	Abbreviated Vita for Leigh Tesfatsion
		It is argued that the Lefschetz approach to fixed point theorems may ultimately prove to be particularly important in economic and game theory due to the generality of spaces that can be considered and the interesting related questions that can be investigated.
		For example, the Lefschetz approach to fixed point theorems leads naturally to the concept of a "Nielsen Number" of a map f:Y->Y, a homotopy-invariant lower bound for the number of fixed points of f.
		This study considers a general class of dynamic investment models in which agents are not restricted to have constant risk aversion.
	www.econ.iastate.edu /tesfatsi/vita.htm (9886 words)

	seminar
		This method is based on the construction of a class of mappings from the space of real-entry matrices to the space of characteristic functions defined on bounded, finite-dimensional geometric regions.
		To understand the cone geometrically, it is necessary to classify its `coextremal rays', generating curve classes of the dual cone corresponding to distinguished fibrations on the variety.
		However they lead to nice max/min problems which tend to pick out distinguished metrics within a conformal class, since one can write a nice (Polyakov) formula for the quotient of such determinants in conformally related metrics; this has been an important theme in string theory.
	www.math.princeton.edu /~seminar/2001-02-sem/2-27-2002weekly.html (1904 words)

	MATH 752 (Site not responding. Last check: 2007-11-02)
		This is the second part of an introductory sequence in topology and geometry which will familiarize students with basic topics and provide preparation for the topology qualifying exam.
		Many areas of modern mathematics require knowledge of topological methods--for example homotopy theory, differential topology play an important role across several subjects.
		A special presentation on applications of topology to problems in engineering/computer science is also contemplated.
	www.math.wisc.edu /~adem/752.html (148 words)

	teaching archive (Site not responding. Last check: 2007-11-02)
		Topology of projective varieties: Weak Lefschetz Theorem, Lefschetz pencils, monodromy, Picard-Lefschetz, relation with the Hard Lefschetz Theorem.
		Students are expected to give in-class presentations on selected related topics/exercises.
		If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748v/TDD.
	www.math.sunysb.edu /~mde/545S_06/545S_06.html (497 words)

	Lefschetz, S.: Topics in Topology. (AM-10).
		Solomon Lefschetz pioneered the field of topology--the study of the properties of manysided figures and their ability to deform, twist, and stretch without changing their shape.
		In Topics in Topology Lefschetz developed a more in-depth introduction to the field, providing authoritative explanations of what would today be considered the basic tools of algebraic topology.
		Lefschetz moved to the United States from France in 1905 at the age of twenty-one to find employment opportunities not available to him as a Jew in France.
	www.pupress.princeton.edu /titles/4017.html (326 words)

	Home (Site not responding. Last check: 2007-11-02)
		Arithmetic dynamics on projective varieties and in particular, arithmetic properties of a certain class of K3 surfaces studied in:
		Wehler, "Hypersurfaces of the Flag Variety: Deformation Theory and the Theorems of Kodaira-Spencer, Torelli, Lefschetz, M. Noether and Serre",
		To help in the transition from class work to research, graduate students at Brown are required to complete a topic exam.
	www.math.brown.edu /~benhutz/research.htm (283 words)

	Volume 22, Number 2, 1996 (Site not responding. Last check: 2007-11-02)
		Markov, Y. Limit cycles of perturbations of a class of quadratic Hamiltonian vector fields.
		The generalized Wiener-Hopf equation and the approximation methods are used to propose a perturbed iterative method to compute the solutions of a general class of nonlinear variational inequalities.
		By means of piecewise continuous functions which are generalizations of the classical Lyapunov's functions, sufficient conditions for the existence of integral manifolds of such equations are found.
	www.math.bas.bg /serdica/n2_96.html (337 words)

	Top 20 Encyclopedia (Site not responding. Last check: 2007-11-02)
		Topology has introduced a new geometric language (simplicial complexes, homotopy, cohomology, Poincaré duality, fibrations, vector bundles, sheaves, characteristic classes, Morse functions, homological algebra, spectral sequences).
		It has had a major impact on the fields of differential geometry, algebraic geometry, dynamical systems and partial differential equations in the large, and several complex variables.
		"Topology", its English form, was introduced in print by Solomon Lefschetz in 1930 to replace the earlier name "analysis situs".
	encyc.connectonline.com /index.php/Topology (1637 words)

	Abstracts and Titles:
		We also obtain the known relationship between higher FR-torsion and the MMM classes on the mapping class group as an easy consequence.
		We will discuss how fairly elementary ideas of calculus can then be used to generalize calculations of Lars Hesselholt and Ib Madsen for Bloch's typical curves ${\rm holim} \tilde K(R[x]/(x^n))$ and a new proof of the calculation by Carlsson, Cohen, Goodwillie and Hsiang of $A(\Sigma X)$ for $X$ a connected space.
		If time permits we will also discuss how the one-parameter Lefschetz class of Geoghegan and Nicas can be reinterpreted in this framework using work of Iwashita.
	www.indiana.edu /~jfdavis/Abstracts_and_Titles.html (506 words)

	Paulo Lima-Filho's Home Page (Site not responding. Last check: 2007-11-02)
		Then we study the cup and cap products and orientation on manifolds.
		Finally, we prove the various important duality theorems due to Poincar\'e, Alexander and Lefschetz.
		The course ends with the Lefschetz fixed point theorem and applications.
	www.math.tamu.edu /~Paulo.Lima-Filho/teaching/m643-f98/hdt1_m643.html (332 words)

	[math/0001105] Lefschetz numbers of iterates of the monodromy and truncated arcs (Site not responding. Last check: 2007-11-02)
		[math/0001105] Lefschetz numbers of iterates of the monodromy and truncated arcs
		Lefschetz numbers of iterates of the monodromy and truncated arcs
		We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs.
	www.arxiv.org /math.AG/0001105 (77 words)

	Preprints: Abstracts (Site not responding. Last check: 2007-11-02)
		An SU(n) Casson invariant of a knot is an integer which can be thought of as an algebraic-topological count of the number of characters of SU(n) representations of the knot group which take a longitude into a given conjugacy class.
		For fibered knots, these invariants can be characterized as Lefschetz numbers which, for generic conjugacy classes, can be computed using a recursive algorithm of Atiyah and Bott, as adapted by Frohman.
		Our technique is based on our discovery that the generating functions associated to the relevant Lefschetz numbers (and polynomials) satisfy certain integral equations.
	www.math.mcmaster.ca /andy/papers/bn.abs.html (182 words)

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