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Geometric group theory and connections to

Lead Research Organisation: University of Southampton
Department Name: School of Mathematics

Abstract

Leary and Minasyan have recently discovered a family of groups with a
surprising set of properties: the groups are CAT(0) and some of them
are not biautomatic and do not have Wise's property. Sam Hughes will
be investigating further properties of these groups. In particular,
comparing them up to isomorphism and up to abstract commensurability
should be interesting.

People

ORCID iD
Sam Hughes (Student)

Publications

10 25 50
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Hughes S (2024) Commensurating HNN-extensions: Hierarchical hyperbolicity and biautomaticity in Commentarii Mathematici Helvetici

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Hughes S (2023) Hyperbolically embedded subgroups and quasi-isometries of pairs in Canadian Mathematical Bulletin

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Hughes S (2023) Quasi-isometry invariance of relative filling functions (with an appendix by Ashot Minasyan) in Groups, Geometry, and Dynamics

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Hughes S (2022) A note on the rational homological dimension of lattices in positive characteristic in Glasgow Mathematical Journal

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Hughes S (2022) Higher topological complexity of hyperbolic groups in Journal of Applied and Computational Topology

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Hughes S (2022) Lattices in a product of trees, hierarchically hyperbolic groups and virtual torsion-freeness. in The bulletin of the London Mathematical Society

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Hughes S (2022) Hyperbolically embedded subgroups and quasi-isometries of pairs

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Hughes S (2022) Cohomology of Fuchsian groups and non-Euclidean crystallographic groups in manuscripta mathematica

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Hughes S (2021) Higher topological complexity of hyperbolic groups

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Chatterji I (2021) The first -betti number and groups acting on trees in Proceedings of the Edinburgh Mathematical Society

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/R513325/1 30/09/2018 29/09/2023
2127970 Studentship EP/R513325/1 30/09/2018 29/09/2021 Sam Hughes