Title: LEIBNIZ FORMULAS FOR CYCLIC HOMOTOPY FIXED POINT SPECTRA
Abstract:We analyze the homotopy xed point spectrum of a T-equivariant com- mutative S-algebra R in homological terms. There is a homological homotopy xed point spectral sequence with E 2 s;t = H s (T;Ht(R;Fp)...We analyze the homotopy xed point spectrum of a T-equivariant com- mutative S-algebra R in homological terms. There is a homological homotopy xed point spectral sequence with E 2 s;t = H s (T;Ht(R;Fp)), which converges condition- ally to the continuous homology H c (R hT ;Fp) of the homotopy xed point spectrum. We show that there are Dyer{Lashof operations Q i acting on this algebra spectral sequence, and that its dieren tials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the E 2r -term of the spectral sequence there are 2r other classes in the E 2r -term (obtained mostly by Dyer{Lashof operations on x) that are innite cycles, i.e., survive to the E 1 -term. We apply this to completely determine the dieren tials in the homological homo- topy xed point spectral sequences for the topological Hochschild homology spectra R = THH(B) of many S-algebras, including B = MU, BP , ku, ko and tmf. Similar results apply for all nite subgroups C T, and for the Tate- and homotopy orbit spectra. This work is part of a homological approach to calculating topological cyclic homology and algebraic K-theory of commutative S-algebras.Read More
Publication Year: 2005
Publication Date: 2005-01-01
Language: en
Type: article
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