Rank 1 phenomena for 1-relator and deficiency 1 groups

J O Button

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arXiv · 2510.15469

Rank 1 phenomena for 1-relator and deficiency 1 groups

J O Button

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Abstract

We examine second bounded cohomology and mod p homology in finite index subgroups of 1-relator groups and groups with a presentation of deficiency at least one. We use this to determine exactly which 1-relator groups are boundedly generated, as well as the groups of deficiency at least one up to a class of groups that conjecturally do not exist.

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J O Button. 2025-10-17. Rank 1 phenomena for 1-relator and deficiency 1 groups. https://arxiv.org/abs/2510.15469

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