Cobordism, spin structures, and profinite completions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908754980634624 |
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| author | Hughes, Sam Ng, Andrew |
| author_facet | Hughes, Sam Ng, Andrew |
| contents | Let $M$ and $N$ be smooth closed connected aspherical manifolds with good (in the sense of Serre) fundamental groups $G$ and $H$. We show that if $\widehat G\cong \widehat H$, then $M$ and $N$ are cobordant and the signatures of $M$ and $N$ agree modulo $8$. Moreover, $M$ is spin (resp.spin$^\CC$) if and only if $N$ is spin (resp.spin$^\CC$). We consider some analogous results for compact connected aspherical manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05706 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cobordism, spin structures, and profinite completions Hughes, Sam Ng, Andrew Group Theory Algebraic Topology Geometric Topology Let $M$ and $N$ be smooth closed connected aspherical manifolds with good (in the sense of Serre) fundamental groups $G$ and $H$. We show that if $\widehat G\cong \widehat H$, then $M$ and $N$ are cobordant and the signatures of $M$ and $N$ agree modulo $8$. Moreover, $M$ is spin (resp.spin$^\CC$) if and only if $N$ is spin (resp.spin$^\CC$). We consider some analogous results for compact connected aspherical manifolds. |
| title | Cobordism, spin structures, and profinite completions |
| topic | Group Theory Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2601.05706 |