Sheaf Theory / Edition 2

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This book is 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. There are several innovations in this book. The concept of the "tautness" of a subspace is introduced and exploited throughout the book. The fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces. Relative cohomology is introduced into sheaf theory. The reader should have a thorough background in elementary homological algebra in an algebraic topology. A list of exercises at the end of each chapter will help the student to learn the material and solutions of many of the exercises are given in an Appendix. The new edition of this classic in the field has been substantially rewritten with the addition of over 80 examples and of further explanatory material. Among the items added are new sections on Cech cohomology, the Oliver transfer, intersection theory, generalized manifolds, locally homogeneous spaces, homological fibrations and p-adic transformation groups.
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Product Details

  • ISBN-13: 9780387949055
  • Publisher: Springer New York
  • Publication date: 2/1/1997
  • Series: Graduate Texts in Mathematics Series , #170
  • Edition description: 2nd ed. 1997
  • Edition number: 2
  • Pages: 504
  • Product dimensions: 1.19 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

I Sheaves and Presheaves 1
II Sheaf Cohomology 33
III Comparison with Other Cohomology Theories 179
IV Applications of Spectral Sequences 197
V Borel-Moore Homology 279
VI Cosheaves and Cech Homology 417
A Spectral Sequences 449
B Solutions to Selected Exercises 455
Bibliography 487
List of Symbols 491
List of Selected Facts 493
Index 495
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