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Geometric Group Theory Seminar - Devin Murray

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February 23, 2017
1:50PM - 2:45PM
Baker Systems Engineering 136

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Add to Calendar 2017-02-23 13:50:00 2017-02-23 14:45:00 Geometric Group Theory Seminar - Devin Murray Title: The morse boundary determines CAT(0) groups up to quasi-isometrySpeaker: Devin Murray (Brandeis University)Abstract: The boundary of hyperbolic space is an important invariant in classical hyperbolic geometry and it plays a pivotal role in many rigidity theorems. The Gromov boundary has played a similar role in the study of delta-hyperbolic groups. In particular, the Gromov boundary of a delta hyperbolic group determines the group up to quasi-isometry type. While CAT(0) spaces also have a notion of a boundary, the topological type of this boundary is not a quasi-isometry invariant and is therefor not well defined for a CAT(0) group. This is where the morse boundary for CAT(0) groups comes in. It was introduced by Charney and Sultan who showed that it is a QI invariant and thus a well defined notion for a CAT(0) group. The morse boundary, equipped with some extra data, completely determines a CAT(0) group. I will talk about the ingredients needed to prove this fact and time permitting I will discuss some about how this fits into other questions about QI rigidity. Baker Systems Engineering 136 Department of Mathematics math@osu.edu America/New_York public

Title: The morse boundary determines CAT(0) groups up to quasi-isometry

Speaker: Devin Murray (Brandeis University)

Abstract: The boundary of hyperbolic space is an important invariant in classical hyperbolic geometry and it plays a pivotal role in many rigidity theorems. The Gromov boundary has played a similar role in the study of delta-hyperbolic groups. In particular, the Gromov boundary of a delta hyperbolic group determines the group up to quasi-isometry type. While CAT(0) spaces also have a notion of a boundary, the topological type of this boundary is not a quasi-isometry invariant and is therefor not well defined for a CAT(0) group. This is where the morse boundary for CAT(0) groups comes in. It was introduced by Charney and Sultan who showed that it is a QI invariant and thus a well defined notion for a CAT(0) group. The morse boundary, equipped with some extra data, completely determines a CAT(0) group. I will talk about the ingredients needed to prove this fact and time permitting I will discuss some about how this fits into other questions about QI rigidity.

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