TY - BOOK ID - 6771030 TI - Sheaves in topology PY - 2004 SN - 3540206655 3642188680 9783540206651 PB - Berlin Heidelberg New York : Springer, DB - UniCat KW - Sheaf theory KW - 515.14 KW - Cohomology, Sheaf KW - Sheaf cohomology KW - Sheaves, Theory of KW - Sheaves (Algebraic topology) KW - Algebraic topology KW - Mathematics KW - Physical Sciences & Mathematics KW - Geometry KW - 515.14 Algebraic topology KW - Sheaf theory. KW - Topologie algébrique KW - Faisceaux, Théorie des KW - Algebraic topology. KW - Algebraic geometry. KW - Functions of complex variables. KW - Algebraic Topology. KW - Algebraic Geometry. KW - Several Complex Variables and Analytic Spaces. KW - Complex variables KW - Elliptic functions KW - Functions of real variables KW - Algebraic geometry KW - Topology KW - Topologie algébrique KW - Faisceaux, Théorie des KW - Faisceaux KW - Geometrie algebrique KW - Topologie algebrique KW - Cohomologie KW - Homologie et cohomologie UR - https://www.unicat.be/uniCat?func=search&query=sysid:6771030 AB - 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. ER -