The transfer and compact Lie groups

Feshbach, Mark

doi:10.1090/S0002-9947-1979-0531973-8

The transfer and compact Lie groups
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by Mark Feshbach

Trans. Amer. Math. Soc. 251 (1979), 139-169

DOI: https://doi.org/10.1090/S0002-9947-1979-0531973-8

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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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