Computer-assisted methods in Sigma-theory

Elisa Hartmann

Computer-assisted methods in Sigma-theory

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arxiv 2407.09264 v3 pith:SMOUVT74 submitted 2024-07-12 math.GR math.AT

Elisa Hartmann This is my paper · ORCID

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keywords charactergroupjustmathrmsigmatypealgorithmambient

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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.

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Geometric invariants of locally compact groups: the homological perspective
math.AT 2024-11 conditional novelty 7.0 of 10

Homological Sigma-invariants are defined for locally compact Hausdorff groups and shown to recover and extend the classical discrete-group invariants.

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