Volume 14, issue 2 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Homology operations in the topological cyclic homology of a point

Håkon Schad Bergsaker and John Rognes

Geometry & Topology 14 (2010) 755–772
Abstract

We consider the commutative S–algebra given by the topological cyclic homology of a point. The induced Dyer–Lashof operations in mod p homology are shown to be nontrivial for p = 2, and an explicit formula is given. As a part of the calculation, we are led to compare the fixed point spectrum SG of the sphere spectrum and the algebraic K–theory spectrum of finite G–sets, as structured ring spectra.

Keywords
topological cyclic homology, homology operation, algebraic $K$–theory
Mathematical Subject Classification 2010
Primary: 55S12, 55P43
Secondary: 19D55, 55P92, 19D10
References
Publication
Received: 18 November 2008
Revised: 11 December 2009
Accepted: 6 December 2009
Published: 19 February 2010
Proposed: Ralph Cohen
Seconded: Haynes Miller, Paul Goerss
Authors
Håkon Schad Bergsaker
Department of Mathematics
University of Oslo
Oslo
Norway
John Rognes
Department of Mathematics
University of Oslo
Oslo
Norway