Sheaves in topology

Alexandru Dimca - Collection Universitext

240 pages, parution le 01/04/2004

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Résumé

Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds, a great geometrical idea due to R. Thom and H. Whitney. These sheaves, generalizing the local systems that are so ubiquitous in mathematics, have powerful applications to the topology of such singular spaces (mainly algebraic and analytic complex varieties). This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant)coefficients. The first 5 chapters introduce derived categories, direct and inverse images of sheaf complexes, Verdier duality, constructible and perverse sheaves, vanishing and characteristic cycles. They also discuss relations to D-modules and intersection cohomology. Later chapters apply this powerful tool to the study of the topology of singularities, polynomial functions and hyperplane arrangements. Some fundamental results, for which excellent sources exist, are not proved but just stated and illustrated by examples and corollaries. In this way, the reader is guided rather quickly from the basic theory to current research questions, supported in this by examples and exercises.

Sommaire

Derived Categories
Derived Categories in Topology
Poincaré
Verdier Duality
Constructible Sheaves, Vanishing Cycles and Characteristic Varieties
Perverse Sheaves
Applications to the Geometry of Singular Spaces

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Alexandru Dimca
Collection	Universitext
Parution	01/04/2004
Nb. de pages	240
Format	15,5 x 23,5
Couverture	Broché
Poids	391g
Intérieur	Noir et Blanc
EAN13	9783540206651