The transfer and compact Lie groups
Author:
Mark Feshbach
Journal:
Trans. Amer. Math. Soc. 251 (1979), 139-169
MSC:
Primary 57R10; Secondary 55M20
DOI:
https://doi.org/10.1090/S0002-9947-1979-0531973-8
MathSciNet review:
531973
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let G be a compact Lie group with H and K arbitrary closed subgroups. Let BG, BH, BK be l-universal classifying spaces, with the natural projection. Then transfer homomorphisms
are defined for h an arbitrary cohomology theory. One of the basic properties of the transfer for finite coverings is a double coset formula. This paper proves a double coset theorem in the above more general context, expressing
as a sum of other compositions. The main theorems were announced in the Bulletin of the American Mathematical Society in May 1977.
- [B] J. C. Becker, Characteristic classes and 𝐾-theory, Algebraic and geometrical methods in topology (Conf. Topological Methods in Algebraic Topology, State Univ. New York, Binghamton, N.Y., 1973), Springer, Berlin, 1974, pp. 132–143. Lecture Notes in Math., Vol. 428. MR 0377877
- [BG] J. C. Becker and D. H. Gottlieb, Transfer maps for fibrations and duality, Compositio Math. 33 (1976), no. 2, 107–133. MR 436137
- [Br] Glen E. Bredon, Introduction to compact transformation groups, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 46. MR 0413144
- [BM] G. Brumfiel and I. Madsen, Evaluation of the transfer and the universal surgery classes, Invent. Math. 32 (1976), no. 2, 133–169. MR 413099, https://doi.org/10.1007/BF01389959
- [CE] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
- [D0] Albrecht Dold, The fixed point transfer of fibre-preserving maps, Math. Z. 148 (1976), no. 3, 215–244. MR 433440, https://doi.org/10.1007/BF01214520
- [D1] Albrecht Dold, Transfert des points fixes d’une famille continue d’applications, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1291–1293 (French). MR 0348734
- [D2] Albrecht Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965), 1–8. MR 193634, https://doi.org/10.1016/0040-9383(65)90044-3
- [I] Sören Illman, Equivariant singular homology and cohomology for actions of compact Lie groups, Proceedings of the Second Conference on Compact Transformation Groups (Univ. Massachusetts, Amherst, Mass., 1971) Springer, Berlin, 1972, pp. 403–415. Lecture Notes in Math., Vol. 298. MR 0377858
- [P] Richard S. Palais, The classification of 𝐺-spaces, Mem. Amer. Math. Soc. No. 36, 1960. MR 0177401
- [Y] C. T. Yang, The triangulability of the orbit space of a differentiable transformation group, Bull. Amer. Math. Soc. 69 (1963), 405–408. MR 146291, https://doi.org/10.1090/S0002-9904-1963-10947-7
Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R10, 55M20
Retrieve articles in all journals with MSC: 57R10, 55M20
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1979-0531973-8
Article copyright:
© Copyright 1979
American Mathematical Society