2011/04/18 by Thomas Haettel, Haettel, Thomas
Mathematics · #32G15 #32J05 #53C35 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1104.3417
openalex publication_date 2011/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a compactification of symmetric spaces of noncompact type, seen as\nspaces of isometry classes of marked lattices, analogous to the Thurston\ncompactification of the Teichm "uller space, and we show that it is\nequivariantly isomorphic to a Satake compactification. We then use it to define\na new compactification of the Torelli space of a hyperbolic surface with marked\npoints, and we show that it is equivariantly isomorphic to the Satake\ncompactification of the image of the period mapping. Finally, we describe the\nnatural stratification of a subset of the boundary.\n