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Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
Ideal triangulations of hyperbolic manifolds
Daryl Cooper
UCSB
Friday, October 14, 2011, 4:00 p.m.
Room 6635 South Hall
Abstract: In dimensions 2 and 3 hyperbolic manifolds can be "triangulated" with
ideal simplices whose vertices are at infinity. The situation is a bit subtle since the
union of these simplices omits a certain subset of the manifold of measure zero. This
subset is a geodesic lamination, a generalization of the idea of finite closed (periodic)
geodesic. In dimension 2 there is only one shape of ideal 2-simplex (triangle) and
there are parameters that describe how these are "glued" giving a parameterization
of Teichmuller space. In dimension 3 an ideal 3-simplex (tetrahedron) has shape
which is a complex number and these must satisfy certain glueing equations: one
per edge of the triangulation. These are related to ideas of Fock and Goncharov for
studying higher Teichmuller spaces, and triangulations are used by Dimofte, Gaiotto
and Gukov to construct Gauge theories.
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