Vanishing of Topological Invariants For Unnormalized Schatten $p$ multiplicative Maps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908676314365952 |
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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 |