Weil-Petersson geometry of Teichmuller-Coxeter complex and its finite rank property

Details Weil-Petersson geometry of Teichmuller-Coxeter complex and its finite rank property Weil-Petersson geometry of Teichmuller-Coxeter complex and its finite rank property

2008-05-18

arxiv.org/abs/0805.2762v2

Mathematics

Differential Geometry

31pages, new version contains a few typos corrected, and a minor modification

Scientific paper

We construct a Weil-Petersson geodesic completion of Teichmuller space
through the formalism of Coxeter complex with the Teichmuller space as its
non-linear non-homogeneous fundamental domain. We show that the metric and
geodesic completions both satisfy a finite rank property, demonstrating a
similarity with the non-compact symmetric spaces of semi-simple Lie groups.

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