Secondary Stiefel-Whitney numbers and corresponding cobordism groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917130980556800 |
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| author | Lavrukhin, Viktor |
| author_facet | Lavrukhin, Viktor |
| contents | For every relation $R$ between Stiefel-Whitney numbers of closed $(n+1)$-manifolds we consider an associated invariant $\varkappa_R$ of null-cobordant $n$-manifolds with a certain additional structure. For $n=2k-1$ and $R = w_{n+1}+v_k^2$ the invariant $\varkappa_R$ equals the Kervaire semi-characteristic. In addition, we construct the cobordism group $Ω_n^R$, which extends the unoriented cobordism group $Ω_n^O$. We show that $\varkappa_R$ is a complete invariant of $R$-cobordism classes of null-cobordant $n$-manifolds. We prove that our invariant $\varkappa_R$ and $R$-cobordism class of manifold are quadratic in the sense of Gusarov-Vassiliev-Podkorytov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Secondary Stiefel-Whitney numbers and corresponding cobordism groups Lavrukhin, Viktor Algebraic Topology Geometric Topology For every relation $R$ between Stiefel-Whitney numbers of closed $(n+1)$-manifolds we consider an associated invariant $\varkappa_R$ of null-cobordant $n$-manifolds with a certain additional structure. For $n=2k-1$ and $R = w_{n+1}+v_k^2$ the invariant $\varkappa_R$ equals the Kervaire semi-characteristic. In addition, we construct the cobordism group $Ω_n^R$, which extends the unoriented cobordism group $Ω_n^O$. We show that $\varkappa_R$ is a complete invariant of $R$-cobordism classes of null-cobordant $n$-manifolds. We prove that our invariant $\varkappa_R$ and $R$-cobordism class of manifold are quadratic in the sense of Gusarov-Vassiliev-Podkorytov. |
| title | Secondary Stiefel-Whitney numbers and corresponding cobordism groups |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2512.06371 |