Transfer in generalized cohomology theories / Fred W. Roush.

Format:

Book

Author/Creator:

Roush, Fred William.

Series:

Pure and applied mathematics (Akadémiai Kiadó)

Pure and applied mathematics

Language:

English

Subjects (All):

Homology theory.

Physical Description:

158 pages ; 24 cm.

Place of Publication:

Budapest : Akadémiai Kiadó, 1999.

Summary:

The standard invariant, homology, of topological spaces was generalized in the 1950s and 1960s to similar invariants into abelian groups, K-Theory, cobordism, and stable homotopy, and such theories were axiomatized under the name generalized cohomology theories, as having properties like exact sequences, homotopy invariance, and excision. If there is a map f from X to Y of topological spaces, there is an induced map on homology, H* (X) to H* (Y) (or backwards in cohomology). Transfer is a mapping in the reverse direction which exists for covering maps (and some other maps), special kinds of locally one to one maps. It is important in studying coverings and actions of finite groups. In this book after the necessary background on generalized cohomology and related topics, it is proved that transfer exists and is unique in all generalized cohomology theories having the properties that one would expect.

Contents:

2. Coverings and Fiber Bundles 12

3. Stable Homotopy Theory: Categories of Spectra 17

4. Generalized Cohomology Theories 27

5. Transfer in Ordinary Cohomology, K-Theory, and Bordism 50

6. Statement of the Main Theorem 58

7. Transfer and Wreath Operations 61

8. Proof of the Elementary Properties of Transfer 75

9. Transfer and Dyer-Lashof Operations 82

10. Transfer and Characteristic Classes 90

11. Computation of Functional Operations Associated with Transfer 99

12. Dyer-Lashof Operations in the Homology of Two-Stage Postnikov Systems 103

13. Transfer Composed with Restriction 112

14. Transfer in Stable Homotopy 127

15. Appendix: Some Later Results 151.

Notes:

Includes bibliographical references (pages 153-156) and index.

ISBN:

9630576503

OCLC:

43452161