McShane-type identities for affine deformations
Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2029-2041.

We derive an identity for Margulis invariants of affine deformations of a complete orientable one-ended hyperbolic surface following the identities of McShane, Mirzakhani and Tan–Wong–Zhang. As a corollary, a deformation of the surface which infinitesimally lengthens all interior simple closed curves must infinitesimally lengthen the boundary.

À partir des identités de McShane, de Mirzakhani et de Tan–Wong–Zhang, nous obtenons une identité pour les invariants de Margulis associés à une déformation affine d’une surface hyperbolique complète, orientable, à un trou. Il en découle le corollaire suivant : une déformation de la surface, dont les courbes simples fermées intérieures s’allongent infinitésimalement, doit également allonger le bord de manière infinitésimale.

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Accepted:
Published online:
DOI: 10.5802/aif.3128
Classification: 57M05, 53C50
Keywords: hyperbolic surface, Margulis spacetime, closed geodesic, McShane identity
Mot clés : surface hyperbolique, espace-temps de Margulis, géodésique fermée, identité de McShane
Charette, Virginie 1; Goldman, William M. 2

1 Département de mathématiques Université de Sherbrooke Sherbrooke, Québec J1K 2R1 (Canada)
2 Department of Mathematics University of Maryland College Park, MD 20742 (USA)
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Charette, Virginie; Goldman, William M. McShane-type identities for affine deformations. Annales de l'Institut Fourier, Volume 67 (2017) no. 5, pp. 2029-2041. doi : 10.5802/aif.3128. http://www.numdam.org/articles/10.5802/aif.3128/

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