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The affine deformation space of a rank two Schottky group: a picture gallery

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Abstract

The Margulis invariant of an affine hyperbolic element measures the signed Lorentzian displacement along the unique closed geodesic in its class. Given a group of affine transformations of Minkowski spacetime whose linear part is Schottky, the Margulis invariant is a useful tool in determining properness of its action. This paper, based on a presentation given at CGG IV Oostende 2005, describes the affine deformation space of a rank two Schottky group. Several illustrations are included, contrasting the difference between the case of a three-holed sphere and that of a one-holed torus.

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Authors and Affiliations

  1. Département de mathématiques, Université de Sherbrooke, 2500 boul. de l’Université, Sherbrooke, QC, Canada, J1K 2R1

    Virginie Charette

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  1. Virginie Charette
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Correspondence to Virginie Charette.

Additional information

Paper based on a presentation given at CGG IV Oostende 2005. Attendance of the conference and the subsequent writing of this paper was made possible by an NSERC Discovery Grant.

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Charette, V. The affine deformation space of a rank two Schottky group: a picture gallery. Geom Dedicata 122, 173–183 (2006). https://doi.org/10.1007/s10711-007-9125-0

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  • DOI: https://doi.org/10.1007/s10711-007-9125-0

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