On the Adams isomorphism for equivariant orthogonal spectra
| Autor: | Reich, Holger, Varisco, Marco |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Algebr. Geom. Topol. 16 (2016), no. 3, 1493-1566 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/agt.2016.16.1493 |
| Popis: | We give a natural construction and a direct proof of the Adams isomorphism for equivariant orthogonal spectra. More precisely, for any finite group G, any normal subgroup N of G, and any orthogonal G-spectrum X, we construct a natural map A of orthogonal G/N-spectra from the homotopy N-orbits of X to the derived N-fixed points of X, and we show that A is a stable weak equivalence if X is cofibrant and N-free. This recovers a theorem of Lewis, May, and Steinberger in the equivariant stable homotopy category, which in the case of suspension spectra was originally proved by Adams. We emphasize that our Adams map A is natural even before passing to the homotopy category. One of the tools we develop is a replacement-by-Omega-spectra construction with good functorial properties, which we believe is of independent interest. Comment: Final version, to appear in Algebraic & Geometric Topology. 58 pages |
| Databáze: | arXiv |
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