Abstract
This note is concerned with stable G-equivariant homology and cohomology theories (G a compact Lie group). In important cases, when H-equivariant theories are defined naturally for all closed subgroups H of G, we show that the G-(co)homology groups of G xH X are isomorphic with H-(co)homology groups of X. We introduce the concept of orientability of G-vector bundles and manifolds with respect to an equivariant cohomology theory and prove a duality theorem which implies an equivariant analogue of Poincaré-Lefschetz duality.
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The ideas developed here partly originate from suggestions made by T. tom Dieck, who introduced me to the subject.
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Wirthmüller, K. Equivariant homology and duality. Manuscripta Math 11, 373–390 (1974). https://doi.org/10.1007/BF01170239
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DOI: https://doi.org/10.1007/BF01170239