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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.18021 |
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| _version_ | 1866916590138687488 |
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| author | Luo, Yuetong |
| author_facet | Luo, Yuetong |
| contents | Let $M$ be a closed spin manifold and $N$ be a codimension 1 submanifold of it. Given certain homotopy conditions, Zeidler shows that the Rosenberg index of $N$ is an obstruction to the existence of positive scalar curvature on $M$. He further gives a transfer map between the K groups of the group $C^*$ algebras of the foundemental group. The transfer map maps the Rosenberg index of $M$ to the one of $N$. In this note, we present an alternative formulation of the transfer map using maps between $C^*$ algebras, and give an analogus result for the codimension 1 transfer of higher K theoretic signatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Codimension 1 transfer maps of K theoretic indexes Luo, Yuetong K-Theory and Homology 19K56 (Primary), 46L80 (Secondary) Let $M$ be a closed spin manifold and $N$ be a codimension 1 submanifold of it. Given certain homotopy conditions, Zeidler shows that the Rosenberg index of $N$ is an obstruction to the existence of positive scalar curvature on $M$. He further gives a transfer map between the K groups of the group $C^*$ algebras of the foundemental group. The transfer map maps the Rosenberg index of $M$ to the one of $N$. In this note, we present an alternative formulation of the transfer map using maps between $C^*$ algebras, and give an analogus result for the codimension 1 transfer of higher K theoretic signatures. |
| title | Codimension 1 transfer maps of K theoretic indexes |
| topic | K-Theory and Homology 19K56 (Primary), 46L80 (Secondary) |
| url | https://arxiv.org/abs/2501.18021 |