Equivariant fibrations and transfer

Author:
Stefan Waner

Journal:
Trans. Amer. Math. Soc. **258** (1980), 369-384

MSC:
Primary 55P99; Secondary 55R05, 57S15

MathSciNet review:
558179

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The basic properties of equivariant fibrations are described, including an equivariant version of the Ďold Theorem. The foundations of equivariant stable homotopy theory are described, and the theory of equivariant transfer is developed.

**[Be1]**J. C. Becker and D. G. Gottlieb,*Transfer and duality*, Purdue Univ. (preprint).**[Di1]**Tammo tom Dieck,*The Burnside ring and equivariant stable homotopy*, Department of Mathematics, University of Chicago, Chicago, Ill., 1975. Lecture notes by Michael C. Bix. MR**0423389****[Ma1]**J. P. May,*Homotopic foundations of algebraic topology*, University of Chicago, Chicago, Ill., (mimeographed notes).**[Ma2]**J. Peter May,*Classifying spaces and fibrations*, Mem. Amer. Math. Soc.**1**(1975), no. 1, 155, xiii+98. MR**0370579****[MHW]**J. P. May, H. Hauschild and S. Waner,*Equivariant infinite loop spaces*(in preparation).**[Mi1]**John Milnor,*On spaces having the homotopy type of a 𝐶𝑊-complex*, Trans. Amer. Math. Soc.**90**(1959), 272–280. MR**0100267**, 10.1090/S0002-9947-1959-0100267-4**[Ni1]**G. Nishida,*On the equivariant J-groups and equivariant stable homotopy types of representations of finite groups*, Kyoto (preprint).**[Sc1]**R. Schön,*Fibrations over a CW*h-*base*, Proc. Amer. Math. Soc.**62**(1977), 165-166.**[St1]**James Stasheff,*A classification theorem for fibre spaces*, Topology**2**(1963), 239–246. MR**0154286****[Wa1]**Stefan Waner,*Equivariant homotopy theory and Milnor’s theorem*, Trans. Amer. Math. Soc.**258**(1980), no. 2, 351–368. MR**558178**, 10.1090/S0002-9947-1980-0558178-7**[Wa2]**-,*Classification of equivariant fibrations*, Trans. Amer. Math. Soc. (to appear)**[Wa3]**-,*The equivariant approximation theorem*, Princeton Univ. (preprint).**[Wa4]**-,*Cyclic group actions and the Adams conjecture*, Princeton Univ. (preprint).**[Wi1]**Klaus Wirthmüller,*Equivariant 𝑆-duality*, Arch. Math. (Basel)**26**(1975), no. 4, 427–431. MR**0375297**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
55P99,
55R05,
57S15

Retrieve articles in all journals with MSC: 55P99, 55R05, 57S15

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1980-0558179-9

Keywords:
*G*-fibrations,
fiberwise,
equivalence,
stable *G*-equivalence,
isotopy subgroup,
transfer,
fiberwise *G*-duality,
equivariant cohomology

Article copyright:
© Copyright 1980
American Mathematical Society