Explicit moduli for closed genus 2 surfaces

Iain Aitchison (University of Melbourne)

Monday 15th February, 2010 16:00-17:00 Mathematics Building, room 204


We explicitly describe the Teichmuller and Moduli spaces for closed surfaces of genus 2: (Compactified) Teichm¨uller space is tiled by copies of 10 explicit 6-dimensional polyhedra, each parametrizing the possible realizations in hyperbolic geometry of a Delauney triangulation/circle pattern with one of 10 specified underlying graphs. This gives the first explicit cell decomposition of the (compactified) moduli space of any closed hyperbolic surface. (Joint with Armando Rodado.)

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