Department of Mathematics

Geometry and Topology

  •  Thurston's metric on Teichmueller spaces of flat n-tori
  •  09/07/2017
  •  2:00 PM - 3:00 PM
  •  C304 Wells Hall
  •  Mark Greenfield, University of Michigan

Several interesting metrics have been defined for Teichmueller spaces of hyperbolic surfaces. However, analogous metrics on the Teichmueller space of flat n-tori have not been as well studied. After reviewing some background on Teichmueller theory, we will define an analog of Thurston's metric for these spaces. We find that in dimension n=2, it agrees with the hyperbolic metric. In particular, this gives a new way to realize the hyperbolic plane as the moduli space of marked flat tori. Time permitting, we will describe the corresponding situation in dimension n>2. This work is joint with Lizhen Ji.

 

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