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Pré-Publication, Document De Travail Année : 2023

Groups with exotic finiteness properties from complex Morse theory

Pierre Py

Résumé

Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of K\"ahler 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 K\"ahler groups with exotic finiteness properties.

Dates et versions

hal-04232760 , version 1 (09-10-2023)

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Claudio Llosa Isenrich, Pierre Py. Groups with exotic finiteness properties from complex Morse theory. 2023. ⟨hal-04232760⟩
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