Topological Hochschild homology and the Bass trace conjecture

TY - JOUR

T1 - Topological Hochschild homology and the Bass trace conjecture

AU - Berrick, A. J.

AU - Hesselholt, Lars

PY - 2015/7/1

Y1 - 2015/7/1

N2 - 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.

AB - 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.

U2 - 10.1515/crelle-2013-0051

DO - 10.1515/crelle-2013-0051

M3 - Journal article

SN - 0075-4102

VL - 704

SP - 169

EP - 185

JO - Journal fuer die Reine und Angewandte Mathematik

JF - Journal fuer die Reine und Angewandte Mathematik

ER -