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Transactions of the American Mathematical Society

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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
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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 $ \rho (H,G):BH \to BG$ the natural projection. Then transfer homomorphisms $ T(H,G):h(BH) \to h(BG)$ 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 $ {\rho ^{\ast}}(K,G) \circ T(H,G)$ as a sum of other compositions. The main theorems were announced in the Bulletin of the American Mathematical Society in May 1977.


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  • [B] J. C. Becker, Characteristic classes and K-theory, Algebraic and Geometrical Methods in Topology, (Binghamton Conf., 1973), Lecture Notes in Math., vol. 428, Springer-Verlag, Berlin, 1974, pp. 132-143. MR 0377877 (51:14046)
  • [BG] J. C. Becker and D. Gottlieb, The transfer for fibrations and duality, Compositio Math. 33 (1976), 107-133. MR 0436137 (55:9087)
  • [Br] G. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972. MR 0413144 (54:1265)
  • [BM] G. Brumfiel and I. Madsen, Evaluation of the transfer and the universal surgery classes, Invent. Math. 32 (1976), 133-169. MR 0413099 (54:1220)
  • [CE] H. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956, p. 257. MR 0077480 (17:1040e)
  • [D0] A. Dold, The fixed point transfer of fibre-preserving maps, Math. Z. 148 (1976), 215-244. MR 0433440 (55:6416)
  • [D1] -, Transfert des points fixes d'une famille continue d'applications, C. R. Acad. Sci. Paris Sér. A. 278 (1974), 1291-1293. MR 0348734 (50:1231)
  • [D2] -, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965), 1-8. MR 0193634 (33:1850)
  • [I] S. Illman, Equivariant singular homology and cohomology for actions of compact Lie groups, Proc. Second Conf. on Compact Transformations Groups (Amherst, 1971), Lecture Notes in Math., vol. 298, Springer-Verlag, Berlin, 1972, p. 414. MR 0377858 (51:14027)
  • [P] R. S. Palais, The classification of G-spaces, Mem. Amer. Math. Soc., no. 36 (1960). MR 0177401 (31:1664)
  • [Y] C. T. Yang, The triangulability of the orbit space of a differentiable transformation group, Bull. Amer. Math. Soc. 69 (1963), 405-408. MR 0146291 (26:3813)

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DOI: https://doi.org/10.1090/S0002-9947-1979-0531973-8
Article copyright: © Copyright 1979 American Mathematical Society

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