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Daniel Woodhouse (University of Oxford)
Friday 16 October 2020, 13:45-14:45
Quasi-isometric rigidity of graphs of free groups with cyclic edge groups
- đ¤ Speaker: Daniel Woodhouse (University of Oxford)
- đ Date & Time: Friday 16 October 2020, 13:45 - 14:45
- đ Venue: Zoom: https://maths-cam-ac-uk.zoom.us/j/91636583222
Abstract
Let F be a finitely rank free group. Let w_1 and w_2 be suitable random/generic elements in F. Consider the HNN extension G generated by F and a stable letter t, with relation t w_1 t^{-1} = w_2 . It is known from existing results that G will be 1-ended and hyperbolic. We have shown that G is quasi-isometrically rigid. That is to say that if a f.g. group H is quasi-isometric to G, then G and H are virtually isomorphic. The full result is for finite graphs of groups with virtually free vertex groups and two-ended edge groups, but the statement is more technical—not all such groups are QI-rigid. The main argument involves applying a new proof of Leighton’s graph covering theorem.
This is joint work with Sam Shepherd.
Series This talk is part of the Geometric Group Theory (GGT) Seminar series.
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