ENGLISH

Sheaf Theory

By Glen E. Bredon (auth.)

Book information

Publisher
Springer-Verlag New York
Year
1997
ISBN
9780387949055, 0387949054
DOI
10.1007/978-1-4612-0647-7
LCC
QA612.36 .B74 1997
Open Library ID
OL1004512M
Language
english
Format
DJVU
Filesize
5 MB (5673024 bytes)
Series
Graduate Texts in Mathematics 170
Edition
2
Pages
504\515
Library
Kolxo3
DPI
600
Time added
2010-07-29 05:14:56
Algebraic Topology

Description

This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems. " Sheaves play several roles in this study. For example, they provide a suitable notion of "general coefficient systems. " Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas impor­ tant to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the con­ cept of the "tautness" of a subspace (an adaptation of an analogous no­ tion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The fact that sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a "single space" theory.

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