English

Computer-assisted methods in Sigma-theory

Group Theory 2024-09-24 v3 Algebraic Topology

Abstract

We develop an algorithm for recognizing whether a character belongs to Σm\Sigma^m. In order to apply it we just need to know that the ambient group is of type FPm\mathrm{FP}_m or of type F2\mathrm{F}_2 and that the word problem is solvable for this group. Then finite data is sufficient proof of membership in Σm\Sigma^m, not just for the given character but also for a neighborhood of it.

Keywords

Cite

@article{arxiv.2407.09264,
  title  = {Computer-assisted methods in Sigma-theory},
  author = {Elisa Hartmann},
  journal= {arXiv preprint arXiv:2407.09264},
  year   = {2024}
}
R2 v1 2026-06-28T17:38:39.787Z