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Are free groups of different rank bi-invariantly quasi-isometric?

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  • UserJarosław Kędra (University of Aberdeen)
  • ClockMonday 17 June 2024, 14:30-15:00
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TRHW02 - International Conference

Let F be a free group equipped with the bi-invariant word metric associated with the generating set consisting of the standard generators and their conjugates. I will prove that a homomorphism between free groups of finite rank is a quasi-isometry if and only if it is an isomorphism. This is in contrast with the classical Geometric Group Theory where an inclusion of a finite index subgroup is a quasi-isometry.  I don’t know an example of a quasi-isometry between free groups of different rank. In particular, the question from the title is open. Joint work with Assaf Libman.

This talk is part of the Isaac Newton Institute Seminar Series series.

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