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	SOLOMON LEFSCHETZ (Site not responding. Last check: 2007-10-08)
		Lefschetz was born in Moscow into a Jewish family.
		One of Lefschetz's most widely used results, the Lefschetz fixed-point theorem, asserts that a map f from a "nice" compact space to itself has a fixed point (a point x such that f(x)=x) when a certain numerical invariant (the "Lefschetz number") of f is nonzero.
		Lefschetz was famous for his intuitive style of reasoning and strong opinions.
	www.nadn.navy.mil /Users/math/meh/lefschetz.html (601 words)

	Lefschetz
		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-gap.dcs.st-and.ac.uk /~history/Mathematicians/Lefschetz.html (2029 words)

	Solomon Lefschetz, Undaunted Genius (Site not responding. Last check: 2007-10-08)
		Lefschetz joined the faculty of the University of Kansas in 1913, the year he became a U.S. citizen and married Alice Berg Hayes, who as a special student at Clark received a master's degree in mathematics in 1911.
		Lefschetz's early research in algebraic geometry with innovative use of topological methods earned him the 1919 Bordin Prize of the French Academy of Science and the Bocher Prize of the American Mathematical Society in 1924.
		Lefschetz's distinguished career led to his presidency of the American Mathematical Society and membership in the Royal Society of London and the National Academy of Sciences.
	aleph0.clarku.edu /~djoyce/mathhist/lefschetz_kna.html (518 words)

	Solomon Lefschetz - Wikipedia, the free encyclopedia
		Solomon Lefschetz (3 September 1884-5 October 1972) was a US mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
		He was born in Moscow into a Jewish family (his parents were Turkish citizens) who moved shortly after that to Paris.
		He proved theorems on the topology of hyperplane sections of algebraic varieties, which provide a basic inductive tool (these are now seen as allied to Morse theory, though a Lefschetz pencil of hyperplane sections is a more subtle system than a Morse function because hyperplanes intersect each other).
	en.wikipedia.org /wiki/Solomon_Lefschetz (423 words)

	Nat' Academies Press, Biographical Memoirs V.61 (1992)
		Lefschetz plunged into these and, with a strong French training in basic mathematics, was all set to attack a research topic suggested by Professor Story, namely, to find information about the largest number of cusps that a plane curve of given degree may possess.
		Lefschetz' first position after Clark was an assistantship at the University of Nebraska in 1911; the assistantship was soon transformed into a regular instructorship.
		A symposium in honor of Lefschetz' seventieth birthday was held in Princeton in 1954,6 and in 1965 an international conference in differential equations and dynamical systems was dedicated to him at the University of Puerto Rico.
	www.nap.edu /books/0309047463/html/270.html (3467 words)

	The Princeton Mathematics Community in the 1930s (PMC21) (Site not responding. Last check: 2007-10-08)
		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.
		As I've said, I felt hurried during those two years, and except for the mentioned snatches of conversation with Lefschetz my contacts with the faculty were largely brief and formal, and I didn't come away with any particularly, warm feelings toward them.
	libweb.princeton.edu /libraries/firestone/rbsc/finding_aids/mathoral/pmc21.htm (2058 words)

	Lefschetz coincidence theory for maps between spaces of different dimensions (Site not responding. Last check: 2007-10-08)
		While the coincidence theory of maps between manifolds of the same dimension is well developed, very little is known if the dimensions are different or one of the spaces is not a manifold.
		For the latter, we consider the Lefschetz homomorphism as a certain graded homomorphism of degree (-n) that depends only on the homomorphisms generated by f and g on homology groups.
		It follows that if the Lefschetz homomorphism is not identically 0 then there is an x in X such that f(x)=g(x) (a coincidence).
	users.marshall.edu /~saveliev/Research/LCT/LCT.htm (318 words)

	Lefschetz maps (Site not responding. Last check: 2007-10-08)
		Lefschetz coincidence theory for maps between spaces of different dimensions...
		AMCA: Lefschetz zeta functions of gradients of circle-valued maps by Andrei Paji...
		Kneading operators, sharp determinants, and weighted Lefschetz zeta functions in...
	www.scienceoxygen.com /math/672.html (86 words)

	Solomon Lefschetz -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		In 1924 he was awarded the (Click link for more info and facts about Bôcher Memorial Prize) Bôcher Memorial Prize for his work in mathematical analysis.
		The (Click link for more info and facts about Lefschetz fixed point theorem) Lefschetz fixed point theorem, now a basic result of topology, he developed in papers from 1923 to 1927, initially for (A pipe that has several lateral outlets to or from other pipes) manifolds.
		He was editor of the (Click link for more info and facts about Annals of Mathematics) Annals of Mathematics from 1928 to 1958.
	www.absoluteastronomy.com /encyclopedia/s/so/solomon_lefschetz.htm (356 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.
	pup.princeton.edu /titles/4017.html (318 words)

	Salomon Bochner Lectures, 2004-2005 (Site not responding. Last check: 2007-10-08)
		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.
		The fourth lecture will bring together the two strands of the discussion, showing how the monodromy data of a Lefschetz fibration can be determined explicitly (via the "lifting homomorphism") from that of a plane branch curve.
	math.rice.edu /Calendar/bochner06.html (468 words)

	AMCA: Lefschetz zeta functions of gradients of circle-valued maps by Andrei Pajitnov (Site not responding. Last check: 2007-10-08)
		Let f be a Morse map from a closed manifold M to a circle and let v be a gradient of f.
		There is a naturally arising Lefschetz zeta function, which counts closed orbits of v (each orbit is counted with a weight depending on its index and homology class).
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/c/y/19.htm (271 words)

	Proceedings of the American Mathematical Society (Site not responding. Last check: 2007-10-08)
		Lefschetz fibration with only one singular fiber over a closed (Riemann) surface of genus
		Other results are that every Dehn twist on a closed surface of genus at least three is a product of two commutators and no Dehn twist on any closed surface is equal to a single commutator.
		-, Lefschetz fibrations of genus two - a topological approach, Proceedings of the 37th Taniguchi Symposium on Topology and Teichmüller Spaces, ed.
	80-www.ams.org.library.uor.edu /proc/2001-129-05/S0002-9939-00-05676-8/home.html (283 words)

	MSN Encarta - Search Results - Solomon Lefschetz
		MSN Encarta - Search Results - Solomon Lefschetz
		Lefschetz, Solomon (1884-1972), Russian American engineer and mathematician, a pioneer in developing the algebraic techniques of topology, a word he...
		Exclusively for MSN Encarta Premium Subscribers--quickly search thousands of articles from magazines such as Time, Newsweek, The Atlantic Monthly, and Smithsonian.
	encarta.msn.com /Solomon_Lefschetz.html (126 words)

	Citations: Introduction to Topology - Lefschetz (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Lefschetz, Introduction to Topology, Princeton Univ. Press, Princeton, N.J., 1949.
		Lefschetz, Introduction to Topology, Princeton University Press, Princeton, 1949.
		Solomon Lefschetz, Introduction to Topology, Princeton University Press, Princeton NJ (1949).
	citeseer.ist.psu.edu /context/16304/0 (1603 words)

	Cornell Math - Yi Lin
		We then proceed to examine the equivariant cohomology of a compact strong Lefschetz Hamiltonian manifold (M, \omega) with generalized coefficients and establish a version of the d_G, \delta-lemma for equivariant differential forms with generalized coefficients.
		Consider a compact Hamiltonian circle manifold with the strong Lefschetz property.
		We constructed a family of 6 dimensional compact Hamiltonian S^1 manifold each of which satisfies the strong Lefschetz property itself but has a non-Lefschetz symplectic quotient.
	www.math.cornell.edu /People/PhD/2004Aug/linyi.html (164 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		If the equivariant Lefschetz number 1X (2) D (f) = (-1)nterHS(HDn(f; I)) n=0 is not equal to zero, then there are f-invariant orbits in Xe, moreover the orb* *it types of the invariant orbits may be recovered from D (f).
		Some result of the Lefschetz type in the equivariant setting may be obtained already by applying the ordinary Lefschetz theorem: consider an equivariant map f : Xe !
		However the advantage of using the equivariant homology and equivariant Lefschetz number D (Xe) 2 U(D) is that we obtain the specific information about orbit type of t* *he invariant orbit.
	hopf.math.purdue.edu /ChornyB/ehomology.txt (2978 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		@D, Lefschetz imposes a further restriction on the domain of the intersection pairi* ng: he requires that all of the pairs (@oei, oj) and (oei, @oj) should also be in general posit ion.1 This assumption allows him to prove equation (2.2)by working with one pair of simplices at a ti *me and extending additively.
		The chain-level intersection pairing became temporarily obsolete when the cu* p product was discovered and it was noticed that the intersection pairing in homology cou ld be defined using only Poincar'e duality and the cup product, without any recourse to the c *hain level.
		Their version of the chain-level intersection pairing has the * same domain as Lefschetz's* second definition and is probably equivalent to it.
	hopf.math.purdue.edu /McClure/intersection.txt (5930 words)

	The Universal Functorial Lefschetz Invariant (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Abstract: We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW -complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules.
		It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and L 2 -torsion of mapping tori.
		Key words: Universal functorial Lefschetz invariants, Grothendieck group of endomorphisms of modules, transfer maps...
	citeseer.ist.psu.edu /254587.html (193 words)

	how Lefschetz trace formulae relate to the Riemann-Weil explicit formula
		By then specialising to the motive of an algebraic Hecke character chi, he was lead to a definition of local traces which produces a relation analogous to the Riemann-Weil explicit formula.
		To summarise the summary: A particular Lefschetz trace formula, appropriately specialized, produces a relation analogous to the Riemann-Weil Explicit Formula.
		Andreas Juhl wrote to me "The ideal case would be to understand the explicit formulas (as of the Riemann zeta function) as Lefschetz formulas.
	www.maths.ex.ac.uk /~mwatkins/zeta/WEF-LTF.htm (366 words)

	Transactions of the American Mathematical Society (Site not responding. Last check: 2007-10-08)
		Abstract: In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced by Dold and Llibre, which can be computed from the homology class of the map.
		We show that these numbers contain information about the existence of periodic points of a given period; and, if we assume the map to be transversal, then they give us the exact number of such periodic orbits.
		M. Shub and D. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps, Topology 13 (1974), 189-191.
	www.ams.org /tran/2000-352-10/S0002-9947-00-02608-8/home.html (524 words)

	Talk 2963 data/Spring_1999/0125 (Site not responding. Last check: 2007-10-08)
		In particular he showed that every symplectic 4-manifold admits a smooth Lefschetz pencil, which can be blown up to yield a Lefschetz fibration over S^2.
		Conversely, Gompf showed that every smooth 4-manifold which admits a Lefschetz fibration (with a few exceptions) is in fact symplectic.
		Consequently, one would like to compute the basic invariants (e.g., signature, Euler characteristic, fundamental group) of a smooth 4-manifold using the global monodromy of a given Lefschetz fibration on that 4-manifold.
	www.math.duke.edu /mcal?abstract-2963 (119 words)

	Faculty Senate: Faculty Achievement Database -- Marshall University
		Lefschetz coincidence theory for maps between spaces of different dimensions, Topology Appl.
		Lefschetz coincidence theory for maps between spaces of different dimensions, Annual AMS-MAA Meeting, New Orleans, January 2001.
		Removing coincidences of maps between manifolds with positive codimension, Conference Topological Methods in Nonlinear Analysis, Będlewo, Poland, June 2001.
	www.marshall.edu /senate/achieve/profile.asp?ID=257 (232 words)

	References for Lefschetz (Site not responding. Last check: 2007-10-08)
		J Adem, A sketch of Solomon Lefschetz's life in Mexico (Spanish), Differential equations, Math.
		W Hodge, Solomon Lefschetz, The Lefschetz centennial conference I, Contemp.
		S Lefschetz, Reminiscences of a mathematical immigrant in the United States, Amer.
	www-gap.dcs.st-and.ac.uk /~history/References/Lefschetz.html (218 words)

	Books by Solomon Lefschetz - Algebraic Geometry - 1114246093 online book shop
		He remained there until 1953.In the application of topology to algebraic geometry, he followed the work of Emile Picard, whom he had heard lecture in Paris.
		This artikel Solomon_Lefschetz is licensed under the GNU free Documentation License.
		This artikel Heinz_Hopf is licensed under the GNU free Documentation License.
	isbncheck.com /886694_solomon-lefschetz_1114246093algebraicgeometryonlinebookshop.html (611 words)

	[No title]
		If f:X --->X is a selfmap of a polyhedron and I(f) is the fixed point index of f on all of X, then we show that I minus 1 satisfies the above axioms.
		This gives a new proof of the Normalization Theorem: If f:X --->X is a selfmap of a polyhedron, then I(f) equals the Lefschetz number of f.
		This result is equivalent to the Lefschetz-Hopf Theorem: If f: X --->X is a selfmap of a finite simplicial complex with a finite number of fixed points, each lying in a maximal simplex, then the Lefschetz number of f is the sum of the indices of all the fixed points of f.
	www.lehigh.edu /~dmd1/h3104.txt (1977 words)

	how Connes' (hypothetical) trace formula relates to Lefschetz trace formulae (Site not responding. Last check: 2007-10-08)
		There's a similarity with Deninger's approach here in that a link is suggested between the Riemann-Weil Explicit Formula and Lefschetz formulae
		In a personal communication, A. Juhl wrote "The ideal case would be to understand the explicit formulas (as of the RZF) as Lefschetz formulas.
		On p.28 (Connes?) "...in particular the expected trace formula is not a semi-classical formula but a Lefschetz formula in the spirit of [Atiyah-Bott]"
	www.maths.ex.ac.uk /~mwatkins/zeta/CTF-LTF.htm (197 words)

	Lefschetz class of elliptic pairs, Stéphane Guillermou
		I would like to purchase this specific document for $25.
		[1] M. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes.
		[2] M. Atiyah and R. Bott, A Lefschetz fixed point formula for elliptic complexes.
	projecteuclid.org /Dienst/UI/1.0/Display/euclid.dmj/1077243249 (225 words)

	The Mathematics Genealogy Project - Solomon Lefschetz
		Click here to see the students listed in chronological order.
		According to our current on-line database, Solomon Lefschetz has 24 students and 3667 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	genealogy.math.ndsu.nodak.edu /html/id.phtml?id=7461 (107 words)

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