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Topology/Geometry Seminar
Thursday, September 20, 2007
5:15pm,
150 Hawthorn
Gabriela Schmithuesen
Cornell University
Teichmueller disks of origamis and outer space
Abstract:
An origami is a combinatorial object obtained by gluing Euclidean squares along their edges according to a few simple rules. The
resulting closed surface X carries a natural structure as a translation surface.
Furthermore the tiling by squares defines a covering p: X -> E of the
torus E ramified over at most one point.
This setting gives a holomorphic and isometric embedding of the
Teichmueller space T_{1,1} of once punctured tori into the Teichmueller
space T(X). Its image in T(X) is a special case of a Teichmueller disk;
the projection into moduli space is a Teichmueller curve. Teichmueller
curves have recently attracted remarkable attention in different fields
as dynamical systems and algebraic geometry.
We describe an analogous construction in the Culler-Vogtmann outer
space, which can be considered as the Teichmueller space for metric
graphs, and transfer results between these two settings.
We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2006 semester: Aissa Wade and Wojciech Dorabiala.
