Hyperbolic spaces in Teichmüller spaces

Details Hyperbolic spaces in Teichmüller spaces Hyperbolic spaces in Teichmüller spaces

2011-10-29

arxiv.org/abs/1110.6526v1

Mathematics

Geometric Topology

22 pages

Scientific paper

We prove, for any n, that there is a closed connected orientable surface S so
that the hyperbolic space H^n almost-isometrically embeds into the
Teichm\"uller space of S, with quasi-convex image lying in the thick part. As a
consequence, H^n quasi-isometrically embeds in the curve complex of S.

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