Vanishing of Topological Invariants For Unnormalized Schatten $p$ multiplicative Maps

Fuente: arXiv
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Main Author: Glebe, Forrest
Format: Preprint
Published: 2025
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author Glebe, Forrest
author_facet Glebe, Forrest
contents A result of Dadarlat shows that nonzero even rational cohomology obstructs the matricial stability of many discrete groups. In the author's previous work, 2-cohomology is used to argue that certain groups are not stable in unnormalized Schatten $p$-norms for $p > 1$, although 2-cohomology is known not to obstruct stability in the unnormalized 2-norm in general. The main result of this paper demonstrates that we should not expect $2k$ cohomology to obstruct in the unnormalized Schatten $p$-norm for $p\le k$, because the invariant in Dadarlat's argument vanishes for maps that are asymptotically multiplicative in the Schatten $p$-norm.
format Preprint
id arxiv_https___arxiv_org_abs_2509_25869
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Vanishing of Topological Invariants For Unnormalized Schatten $p$ multiplicative Maps
Glebe, Forrest
Operator Algebras
Group Theory
K-Theory and Homology
A result of Dadarlat shows that nonzero even rational cohomology obstructs the matricial stability of many discrete groups. In the author's previous work, 2-cohomology is used to argue that certain groups are not stable in unnormalized Schatten $p$-norms for $p > 1$, although 2-cohomology is known not to obstruct stability in the unnormalized 2-norm in general. The main result of this paper demonstrates that we should not expect $2k$ cohomology to obstruct in the unnormalized Schatten $p$-norm for $p\le k$, because the invariant in Dadarlat's argument vanishes for maps that are asymptotically multiplicative in the Schatten $p$-norm.
title Vanishing of Topological Invariants For Unnormalized Schatten $p$ multiplicative Maps
topic Operator Algebras
Group Theory
K-Theory and Homology
url https://arxiv.org/abs/2509.25869