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arXiv · 2509.25869

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

Forrest Glebe
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Abstract

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.

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Forrest Glebe. 2025-09-30. Vanishing of Topological Invariants For Unnormalized Schatten $p$ multiplicative Maps. https://arxiv.org/abs/2509.25869

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