Topological Hochschild homology and the Bass trace conjecture
-
A. J. Berrick
and
Lars Hesselholt
Abstract
We use the methods of topological Hochschild homology to shed new light on groups satisfying the Bass trace conjecture. Factorization of the Hattori–Stallings rank map through the Bökstedt–Hsiang–Madsen cyclotomic trace map leads to Linnell's restriction on such groups. As a new consequence of this restriction, we show that the conjecture holds for any group G wherein every subgroup isomorphic to the additive group of rational numbers has nontrivial and central image in some quotient of G.
Funding source: NUS
Award Identifier / Grant number: R-146-000-097-112
Funding source: Singapore Ministry of Education
Award Identifier / Grant number: MOE2010-T2-2-125
Funding source: JSPS
Award Identifier / Grant number: Grant-in-Aid 23340016
Funding source: DNRF Niels Bohr Professorship
This paper was written in part while the second author visited the National University of Singapore. He would like to thank the university for its hospitality and support. He also thanks Holger Reich for helpful discussions.
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Halphen's transform and middle convolution
- The extended Bloch group and algebraic K-theory
- Tits alternatives for graph products
- Counting, mixing and equidistribution of horospheres in geometrically finite rank one locally symmetric manifolds
- Area minimizing surfaces in mean convex 3-manifolds
- Topological Hochschild homology and the Bass trace conjecture
- Sur la présentation des représentations supersingulières de GL2(F)
- Self-similar solutions to the mean curvature flow in the Minkowski plane ℝ1,1
