Groups with exotic finiteness properties from complex Morse theory
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916647336411136 |
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| author | Isenrich, Claudio Llosa Py, Pierre |
| author_facet | Isenrich, Claudio Llosa Py, Pierre |
| contents | Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of Kähler groups and their subgroups. In this work, we push this further and exhibit, for each integer $k$, new hyperbolic groups admiting surjective homomorphisms to $\mathbb{Z}$ and to $\mathbb{Z}^{2}$, whose kernel is of type $\mathscr{F}_{k}$ but not of type $\mathscr{F}_{k+1}$. By a fibre product construction, we also find examples of nonnormal subgroups of Kähler groups with exotic finiteness properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_04073 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Groups with exotic finiteness properties from complex Morse theory Isenrich, Claudio Llosa Py, Pierre Geometric Topology Complex Variables Differential Geometry Group Theory Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of Kähler groups and their subgroups. In this work, we push this further and exhibit, for each integer $k$, new hyperbolic groups admiting surjective homomorphisms to $\mathbb{Z}$ and to $\mathbb{Z}^{2}$, whose kernel is of type $\mathscr{F}_{k}$ but not of type $\mathscr{F}_{k+1}$. By a fibre product construction, we also find examples of nonnormal subgroups of Kähler groups with exotic finiteness properties. |
| title | Groups with exotic finiteness properties from complex Morse theory |
| topic | Geometric Topology Complex Variables Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2310.04073 |