Cobordism, spin structures, and profinite completions
Abstract
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Homotopy and Cohomology in Algebraic Topology
Advanced Operator Algebra Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 January 2026
- Document type
- Preprint