Sheaf Theory [Paperback]

Primarily concerned with the study of cohomology theories of general topological spaces with general coefficient systems , the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the tautness of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.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 Spanls