Computer-assisted methods in Sigma-theory
Abstract
We develop an algorithm for recognizing whether a character belongs to $\Sigma^m$. In order to apply it we just need to know that the ambient group is of type $\mathrm{FP}_m$ or of type $\mathrm{F}_2$ and that the word problem is solvable for this group. Then finite data is sufficient proof of membership in $\Sigma^m$, not just for the given character but also for a neighborhood of it.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2024
- DOI:
- 10.48550/arXiv.2407.09264
- arXiv:
- arXiv:2407.09264
- Bibcode:
- 2024arXiv240709264H
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Algebraic Topology