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Mathematische Annalen

, Volume 336, Issue 1, pp 191–238 | Cite as

Transfer maps and the cyclotomic trace

  • Christian SchlichtkrullEmail author
Article

Abstract

We analyze the equivariant restriction (or transfer) maps in topological Hochschild homology associated to inclusions of group rings of the form R[H]→R[G], where R is a symmetric ring spectrum, G is a discrete group and HG is a subgroup of finite index. This leads to a complete description of the associated restriction (or transfer) maps in topological cyclic homology

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in terms of the well-known stable transfers in equivariant stable homotopy theory. More generally, we analyze the restriction maps encountered in connection with monoid rings such as polynomial rings and truncated polynomial rings. As a first application of these results we prove a conjecture by Bökstedt, Hsiang and Madsen on how the transfer maps in Waldhausen's algebraic K-theory of spaces relate to the transfers in the stable equivariant homotopy category of a finite cyclic group. As a second application we calculate the subgroup of transfer invariant homotopy classes

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and we show that the TC-analogue of the lower K-groups vanish below degree −1.

Keywords

Conjugacy Class Homotopy Group Smash Product Topological Realization Symmetric Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway

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