Constructing proper affine actions via higher strip deformations

Date

2023-05-22

Authors

Žager Korenjak, Neža

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Abstract

We introduce higher strip deformations, which give a way of constructing affine deformations of discrete free groups in the image of the irreducible representation PSL₂ R → SO(2n, 2n − 1). We use the Margulis invariant to fnd a properness condition for these deformations, showing that each convex cocompact free group admits affne deformations acting properly on R [superscript 4n−1]. Using our method we can also construct proper affne actions of virtually free groups, which we demonstrate by fnding proper actions of C₂*C₃3 on R⁷.

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