Sheaf Theory
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Sheaf Theory

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ISBN-13:
9781461206477
Einband:
PDF
Seiten:
0
Autor:
Glen E. Bredon
Serie:
Graduate Texts in Mathematics
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:

This book is primarily concerned with the study of cohomology theories of general topological spaces with "e;general coefficient systems. "e; Sheaves play several roles in this study. For example, they provide a suitable notion of "e;general coefficient systems. "e; 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 "e;tautness"e; 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 "e;single space"e; theory.
This book is primarily concerned with the study of cohomology theories of general topological spaces with "e;general coefficient systems. "e; Sheaves play several roles in this study. For example, they provide a suitable notion of "e;general coefficient systems. "e; 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 "e;tautness"e; 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 "e;single space"e; theory.

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