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DTSTART:20230312T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20231109T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/isometri
 c-embeddings-and-totally-geodesic-submanifolds
SUMMARY:Isometric embeddings and totally geodesic submanifolds of Teichmül
 ler\nspaces
CLASS:PUBLIC
DESCRIPTION:FREDERIK BENIRSCHKE\, UNIVERSITY OF CHICAGO\n\nClassical result
 s by Royden\, Earle\, and Kra imply that the\nbiholomorphism group of Teic
 hmüller space\, the isometry group of the\nTeichmüller metric\, and the 
 mapping class group of the underlying\nsurface are all isomorphic. In othe
 r words\, every isometry of\nTeichmüller space is induced by a homeomorph
 ism of the underlying\nsurface.\n\nIn this talk\, we present a generalizat
 ion\, obtained in joint work with\nCarlos Serván\, where we relax isometr
 ies to isometric embeddings. The\nmain result is that isometric embeddings
  of Teichmüller spaces are\ncoverings constructions\, except for some low
 -dimensional special\ncases. In other words: Isometric embeddings are indu
 ced by branched\ncoverings of the underlying surfaces.\n\nTime permitting\
 , we explain how our techniques can be used to rule out\nthe existence of 
 certain totally geodesic submanifolds.\n\nQNC 2501
DTSTAMP:20260318T081753Z
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