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Topic: Lefschetz pencil

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Solomon Lefschetz

Lefschetz fixed point theorem

Lefschetz number

Lefschetz decomposition

Lefschetz class

Lefschetz pencil

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Lefschetz pencil

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	Solomon Lefschetz Summary
		Lefschetz turned to the study of mathematics, and, as a fellow of Clark University, he earned a doctorate in mathematics in 1911.
		Solomon Lefschetz (3 September 1884 – 5 October 1972) was a U.S. mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations.
		The Lefschetz fixed point theorem, now a basic result of topology, he developed in papers from 1923 to 1927, initially for manifolds.
	www.bookrags.com /Solomon_Lefschetz (555 words)

	Pencil (mathematics) - Wikipedia, the free encyclopedia
		A Pencil is a family of geometric objects, such as lines, that have a common property, such as passage through a given line in a given plane.
		In more technical language, a pencil is the special case of a linear system of divisors in which the parameter space is a projective line.
		Typical pencils of curves in the projective plane, for example, are written as
	en.wikipedia.org /wiki/Pencil_(mathematics) (106 words)

	solomon lefschetz - Article and Reference from OnPedia.com
		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.
		The Lefschetz fixed point theorem, now a basic result of topology, he developed in papers from 1923 to 1927, initially for manifolds.
		Lefschetz, Solomon Lefschetz, Solomon Lefschetz, Solomon Lefschetz, Solomon
	www.onpedia.com /encyclopedia/Solomon-Lefschetz (412 words)

	Seminar on Lefschetz fibrations (Site not responding. Last check: )
		A holomorphic Lefschetz pencil on a complex surface X is a nontrivial holomorphic map from a blow-up of X to the Riemann sphere.
		There are corresponding notions of Lefschetz pencils in the topological and symplectic categories in which the fibres are smooth, respectively symplectic, submanifolds.
		Donaldson's theorem states that every symplectic manifold whose symplectic form is integral admits a symplectic Lefschetz pencil.
	129.187.111.185 /lehrveranstaltungen/Lefschetz.html (252 words)

	mathematical equations - papers and reports on...
		Solomon Lefschetz, touted as one of the most revolutionary mathematicians of all time, played a major role in the progress of American mathematics at the turn of the century and beyond.
		The concept of alternative assessment is the result of concern about what traditional paper and pencil tests really assess.
		Several alternative assessment techniques are explained, including examples from teachers about what types of assessments they are using in their elementary or secondary classrooms.
	www.mathreports.com /categories/136-000.html (1060 words)

	UCI Topology Seminar Fall 1997
		Firstly, one may ask which smooth 4-manifolds are branched covers of a fixed smooth 4-manifold, such as $S^4$ or $S^2 \times S^2.$ Secondly, recent work has shown that every symplectic 4-manifold admits a "canonical" Lefschetz pencil, and conversely that every such pencil admits a symplectic structure.
		Thus the existence of Lefschetz pencils provides a topological characterization of symplectic 4-manifolds.
		We unite these two themes by proving that most smooth Lefschetz fibrations may be obtained as a 3-fold branched cover of $S^2 \times S^2,$ branched over an embedded surface.
	www.math.uci.edu /~rstern/TopologySeminarf97.html (469 words)

	Lefschetz Fibrations in Symplectic Geometry - Donaldson (ResearchIndex) (Site not responding. Last check: )
		Lefschetz Fibrations in Symplectic Geometry - Donaldson (ResearchIndex)
		respectively, state that a smooth 4 manifold is symplectic if and only if it admits a (smooth) Lefschetz pencil.
		0.2: Inequalities related to Lefschetz pencils and integrals of..
	citeseer.ist.psu.edu /donaldson98lefschetz.html (360 words)

	Abstracts of my papers
		This relation induces an elliptic Lefschetz pencil structure on the four-manifold \cp $#(9-k)$ \cpb $ $ with $k$ base points and twelve singular fibers.
		As an application a new proof of the fact that the growth rate of a Dehn twist is linear is given.
		By taking appropriate fiber sums of the corresponding Lefschetz fibrations, we construct, for every $g\geq 2$, infinitely many pairwise nonhomeomorphic smooth $4$-manifolds admitting genus-$g$ Lefschetz fibrations over the $2$-sphere $S^2$ but not carrying any complex structure.
	www.math.metu.edu.tr /~korkmaz/abstracts.html (1508 words)

	GT Vol 5 (2001) Paper 19 (Abstract) (Site not responding. Last check: )
		We study Lefschetz pencils on symplectic four-manifolds via the associated spheres in the moduli spaces of curves, and in particular their intersections with certain natural divisors.
		We prove that pencils of large degree always give spheres which behave `homologically' like rational curves; contrastingly, we give the first constructive example of a symplectic non-holomorphic Lefschetz pencil.
		We also prove that only finitely many values of signature or Euler characteristic are realised by manifolds admitting Lefschetz pencils of genus two curves.
	www.univie.ac.at /EMIS/journals/GT/GTVol5/paper19.abs.html (113 words)

	[No title]
		We will show that the right set up for questions concerning the existence of foliated generic function is that of Levi flat CR manifolds which embed in projective space.
		More generally, the notion of Lefschetz pencil structure (a kind of CR morse function) will be defined.
		If time allows, the relation between the notion of strict C-convexity and Lefschetz pencil structures of the simplest kind will we sketched.
	www.dm.unipi.it /~geom/Abstracts/martinez_abs.txt (91 words)

	Presas' Talk (Site not responding. Last check: )
		Donaldson-Auroux ideas in the symplectic case are briefly reviewed and adapted to the contact case.
		The main results are: construction and topological characterization of contact submanifolds in a given homology class of a contact manifold, definition and construction of pencils of "Lefschetz type" in a contact manifold, adaptation of the discussion to symplectic manifolds with convex boundary.
		Finally, some conjectural invariants will be proposed using the notion of Lefschetz pencil.
	math.stanford.edu /contact/talk/presas.html (92 words)

	Métodos Analíticos Complexos em Sistemas Dinâmicos-Comitê Científico (Site not responding. Last check: )
		Under global hypotheses on the foliation, we show that the foliation is a pencil whose generic element is a Calabi-Yau hypersurface.
		Also we study pencils of codimension two Calabi-Yau varieties induced on some of the hypersurfaces of the pencil.
		In the case of a Lefschetz pencil the relation between the geometric situation and the above context will be explained.
	webold.impa.br /Conferencias/Cesar_Camacho/abstracts_index.html (1680 words)

	Geometry/Topology Seminar
		Abstract: Donaldson has shown that every compact symplectic 4-manifold can be represented as a Lefschetz pencil (i.e., up to blowups, a fibration over the 2-sphere with at most nodal fibers).
		This leads to a description of symplectic 4-manifolds by positive factorizations in mapping class groups.
		Abstract: The classification of symplectic 4-manifolds is closely related to that of Lefschetz fibrations and to that of plane curves with node and cusp singularities.
	www.math.uchicago.edu /~geometry/gt_seminar.W2005.html (907 words)

	[No title] (Site not responding. Last check: )
		abstract: Consider a smooth, closed, orientable 4-manifold X. Auroux, Donaldson and Katzarkov proved that if X has a near-symplectic form, then X is a singular Lefschetz pencil.
		Etnyre and Fuller showed that the connected sum of X and a S^2 bundle over S^2 is an achiral Lefschetz fibration.
		David Gay and I have shown that X is a singular, achiral, Lefschetz fibration.
	www.math.columbia.edu /~petero/morgan60/kirby.html (95 words)

	Talk 2963 data/Spring_1999/0125 (Site not responding. Last check: )
		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)

	Front: [math.AG/0112204] Relative Cohomology with Respect to a Lefschetz Pencil
		Front: [math.AG/0112204] Relative Cohomology with Respect to a Lefschetz Pencil
		Title: Relative Cohomology with Respect to a Lefschetz Pencil
		Abstract: Let $M$ be a complex projective manifold of dimension $n+1$ and $f$ a meromorphic function on $M$ obtained by a generic pencil of hyperplane sections of $M$.
	front.math.ucdavis.edu /0112.5204 (183 words)

	Citebase - Relative Cohomology with Respect to a Lefschetz Pencil
		Citebase - Relative Cohomology with Respect to a Lefschetz Pencil
		Relative Cohomology with Respect to a Lefschetz Pencil
		Let M be a complex projective manifold of dimension n+1 and f a meromorphic function on M obtained by a generic pencil of hyperplane sections of M.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0112204 (238 words)

	[No title]
		More recently, the existence result obtained by Donaldson for symplectic Lefschetz pencil structures on symplectic manifolds has opened a completely new direction in low dimensional symplectic topology, followed by work of Auroux and Katzarkov on the topology of 4-dimensional symplectic manifolds viewed as finite ramified coverings of CP2.
		Lagrangian Floer homology and the homological mirror symmetry conjecture.
		Monodromy invariants of symplectic Lefschetz pencils or branched covering maps, and their relation to other invariants (Seiberg-Witten, Gromov-Witten, Lagrangian Floer homology).
	www.ipam.ucla.edu /programs/sgpws1 (302 words)

	Book 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_1114246093algebraicgeometryo... (611 words)

	Catalog_Mathematics
		Stray underlining in red pencil, pencil notes, no dust jacket, scuffs to boards.
		Notes in first chapter and rear endpaper, all in pencil.
		A few stray pen marks in the table of contents, plus some pencil marks.
	www.georgecrossbooks.com /Catalog_Mathematics.html (3418 words)

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