## Geometry & Topology

### Homology operations in the topological cyclic homology of a point

#### 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.

#### Article information

Source
Geom. Topol., Volume 14, Number 2 (2010), 755-772.

Dates
Revised: 11 December 2009
Accepted: 6 December 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732205

Digital Object Identifier
doi:10.2140/gt.2010.14.755

Mathematical Reviews number (MathSciNet)
MR2602850

Zentralblatt MATH identifier
1204.55014

#### Citation

Bergsaker, Håkon Schad; Rognes, John. Homology operations in the topological cyclic homology of a point. Geom. Topol. 14 (2010), no. 2, 755--772. doi:10.2140/gt.2010.14.755. https://projecteuclid.org/euclid.gt/1513732205

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