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＜電子ブック＞
Sheaves in Topology / by Alexandru Dimca
(Universitext. ISSN:21916675)

版	1st ed. 2004.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2004
本文言語	英語
大きさ	XVI, 240 p : online resource
冊子体	Sheaves in topology / Alexandru Dimca ; : pbk
著者標目	*Dimca, Alexandru author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Algebraic geometry LCSH:Functions of complex variables FREE:Algebraic Topology FREE:Algebraic Geometry FREE:Several Complex Variables and Analytic Spaces
一般注記	1 Derived Categories -- 1.1 Categories of Complexes C*(A) -- 1.2 Homotopical Categories K*(A) -- 1.3 The Derived Categories D*(A) -- 1.4 The Derived Functors of Hom -- 2 Derived Categories in Topology -- 2.1 Generahties on Sheaves -- 2.2 Derived Tensor Products -- 2.3 Direct and Inverse Images -- 2.4 The Adjunction Triangle -- 2.5 Local Systems -- 3 Poincaré-Verdier Duality -- 3.1 Cohomological Dimension of Rings and Spaces -- 3.2 The Functor f! -- 3.3 Poincaré and Alexander Duality -- 3.4 Vanishing Results -- 4 Constructible Sheaves, Vanishing Cycles and Characteristic Varieties -- 4.1 Constructible Sheaves -- 4.2 Nearby and Vanishing Cycles -- 4.3 Characteristic Varieties and Characteristic Cycles -- 5 Perverse Sheaves -- 5.1 t-Structures and the Definition of Perverse -- 5.2 Properties of Perverse -- 5.3 D-Modules and Perverse -- 5.4 Intersection Cohomology -- 6 Applications to the Geometry of Singular Spaces -- Singularities, Milnor Fibers and Monodromy -- Topology of Deformations -- Topology of Polynomial Functions -- Hyperplane and Hypersurface Arrangements -- References 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'', which treats the cohomology of spaces with sheaf coefficients (as opposed to the classical constant coefficient cohomology). The first five 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. The final chapters apply this powerful tool to the study of the topology of singularities, of polynomial functions and of 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 A-B-C of the theory to current research questions, supported in this by a wealth of examples and exercises Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-642-18868-8

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