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Constructing proper affine actions via higher strip deformations

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arxiv 2205.14712 v1 pith:ERARPSA7 submitted 2022-05-29 math.GT math.DGmath.GR

Neža Žager Korenjak This is my paper · ORCID
classification math.GTmath.DGmath.GR
keywords deformationsaffineactionsfreemathbbproperconstructinggroups
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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 $\operatorname{PSL}_2\mathbb{R}\to \operatorname{SO}(2n,2n-1)$. We use the Margulis invariant to find a properness condition for these deformations, showing that each convex cocompact free group admits affine deformations acting properly on $\mathbb{R}^{4n-1}$. Using our method we can also construct proper affine actions of virtually free groups, which we demonstrate by finding proper actions of $C_2 \star C_3$ on $\mathbb{R}^7.$

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bending, entropy and proper affine actions of surface groups

    math.GT 2026-02 conditional novelty 7.0 of 10

    Every non-Fuchsian quasifuchsian surface group in an explicit open neighborhood of the Fuchsian locus admits a proper affine action on sl(2,C) with adjoint linear part, and all entropy critical points in a larger neig...

  2. Affine Anosov representations

    math.DS 2024-12 conditional novelty 2.0 of 10

    This paper is a survey of affine Anosov representations, a framework in which proper affine actions of hyperbolic groups are characterized by Margulis invariant spectra, mostly quoting the author's own results.

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