Quasi-isometric groups with no common model geometry

Emily Stark; Daniel Woodhouse

doi:10.1112/jlms.12189

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arXiv · 1711.05026

Quasi-isometric groups with no common model geometry

Emily Stark·Daniel Woodhouse

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Abstract

A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly and cocompactly by isometries on the same proper geodesic metric space, then the groups are commensurable. Consequently, there are infinitely many fundamental groups of simple surface amalgams that are quasi-isometric, but which do not act properly and cocompactly on the same proper geodesic metric space.

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Emily Stark, Daniel Woodhouse. 2017-11-14. Quasi-isometric groups with no common model geometry. https://doi.org/10.1112/jlms.12189

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