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 important 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 concept of the ""tautness"" of a subspace (an adaptation of an analogous notion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The factthat 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.
By:
Glen E. Bredon Imprint: Springer-Verlag New York Inc. Country of Publication: United States Edition: 2nd ed. 1997. Softcover reprint of the original 2nd ed. 1997 Volume: 170 Dimensions:
Height: 235mm,
Width: 155mm,
Spine: 26mm
Weight: 795g ISBN:9781461268543 ISBN 10: 1461268540 Series:Graduate Texts in Mathematics Pages: 504 Publication Date:28 September 2012 Audience:
Professional and scholarly
,
Undergraduate
Format:Paperback Publisher's Status: Active