Geometry in non-discrete groups of hyperbolic isometries: Primitive stability and the Bowditch Q-conditions are equivalent.

Abstract: There are geometrical conditions on a group of hyperbolic isometries which are of interest even when the group is not discrete. We explain two such conditions; these are stated in terms of the images of primitive elements of the free group \(F_2\) under an \(\textrm{SL}(2,\mathbb{C})\) representation. One is Minsky’s condition of primitive stability; the other is the so-called BQ-conditions introduced by Bowditch and generalised by Tan, Wong, and Zhang.

These two conditions have been shown to be equivalent by Jaijeong Lee and Binbin Xu (Trans AMS 2020) and independently by the speaker (arxiv 2019). We will explain the ideas using an combination of both methods. If time permits, we also explain another, closely related, condition which constrains the axes of palindromic primitive elements.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | paper | slides )

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Geometry and topology online

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The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

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