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Cohomological Methods in Transformation Groups [Minkštas viršelis]

(University of Hawaii, Manoa), (Universität Konstanz, Germany)
  • Formatas: Paperback / softback, 484 pages, aukštis x plotis x storis: 229x152x27 mm, weight: 710 g, Worked examples or Exercises
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 12-Feb-2009
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521101328
  • ISBN-13: 9780521101325
Kitos knygos pagal šią temą:
Cohomological Methods in Transformation GroupsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 484 pages, aukštis x plotis x storis: 229x152x27 mm, weight: 710 g, Worked examples or Exercises
  • Serija: Cambridge Studies in Advanced Mathematics
  • Išleidimo metai: 12-Feb-2009
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521101328
  • ISBN-13: 9780521101325
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780521101325.html
Raktažodžiai:
This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.

Recenzijos

"...a clear, beautifully written presentation of some of the central developments in topology in the last thirty-odd years, centering on a subject which we dare predict will never cease to surprise, namely, the action of groups on topological spaces. May it be the forerunner of several other such expositions." Gian-Carlo Rota, The Bulletin of Mathematical Books "...written in a lucid and careful style. All the areas previously mentioned are discussed (as well as many more), paying special attention to the key elements involved in the proofs. Alternate approaches are often discussed, and many interesting examples are provided. The authors have done an admirable job of explaining this area of mathematics. Thoughtful remarks are included in several places, there are exercises at the end of each chapter, and the references are abundant. Moreover, there are two appendices which provide much of the necessary background in commutative and differential algebra....[ I]t should prove useful to a broad spectrum of mathematicians." Alejandro Adem, Bulletin of the American Mathematical Society

Daugiau informacijos

The reader with a relatively modest background in algebraic topology can penetrate rather deeply into the subject.
Preface ix
Chapter 1 Equivariant cohomology of G-CW-complexes and the Borel construction 1
1.1 G-CW-complexes and a comparison theorem for equivariant cohomology theories
3
1.2 The Borel construction
10
1.3 The Borel construction for 2-tori
22
1.4 The Borel construction for p-tori
61
Exercises
85
Chapter 2 Summary of some aspects of rational homotopy theory 92
2.1 The Sullivan-de Rham algebra
92
2.2 Minimal models
96
2.3 Rational homotopy theory
99
2.4 Finite-dimensional rational homotopy
104
2.5 The Grivel-Halperin-Thomas theorem
106
2.6 Sullivan-de Rham theory for rational Alexander-Spanier cohomology
111
2.7 Formal spaces, formal maps and the Eilenberg-Moore spectral sequence
116
Chapter 3 Localization 129
3.1 The Localization Theorem
130
3.2 The Localization Theorem for general G-spaces
141
3.3 Equivariant rational homotopy
148
3.4 Equivariant rational homotopy for general G-spaces
158
3.5 The Evaluation Theorem for torus actions
160
3.6 The ideals p(K , c)
166
3.7 Chang-Skjelbred modules and Hsiang-Serre ideals
175
3.8 Hsiang's Fundamental Fixed Point Theorem
189
3.9 Remarks on the Weyl group
205
3.10 The cohomology inequalities and other basic results
208
3.11 The Hirsch-Brown model and the Evaluation Theorem for p-torus actions on general spaces
223
Exercises
244
Chapter 4 General results on torus and p-torus actions 253
4.1 Rank and Poincare series
254
4.2 Generalities on torus actions
264
4.3 Almost-free torus actions and the rank of a space
269
4.4 More results on almost-free torus actions
280
4.5 The method of Browder and Gottlieb
286
4.6 Equivariant Tate cohomology
301
4.7 Two theorems on topological symmetry
326
4.8 Localization and the Steenrod algebra
332
4.9 The rational homotopy Lie algebra of a fixed point set
336
Exercises
338
Chapter 5 Actions on Poincare duality spaces 342
5.1 Algebraic preliminaries
343
5.2 Poincare duality for the fixed point set
347
5.3 Equivariant Gysin homomorphism, Euler classes and a formula of A. Borel
360
5.4 Torus actions and Pontryagin classes
383
5.5 Golber formulas and other results
386
Exercises
394
Appendix A Commutative algebra 398
A.1 Krull dimension
399
A.2 Modules
401
A.3 Primary decomposition
405
A.4 Homological dimension
408
A.5 Regular sequences
413
A.6 Cohen-Macaulay rings and modules
418
A.7 Evaluations and presentations
425
Appendix B Some homotopy theory of differential modules 435
B.1 Basic notions and elementary results
436
B.2 Applications to cochain complexes over graded algebras
448
Exercises
454
References 456
Index 466
Index of Notation 469