Geometric Group Theory Seminar
Title: Manhattan curves and manifolds and metric structures on hyperbolic groups
Speaker: Eduardo Reyes
University: Yale University
Abstract:
Hyperbolic groups are generalizations of finitely generated free groups and surface groups, and act properly and cocompactly by isometries on Gromov hyperbolic spaces. For a fixed hyperbolic group, we can pack all its actions of this type into a single space, called space of metric structures, which extends the classically studied Teichmuller and Outer spaces but contains many more interesting actions. I will talk about the geometry of this space when equipped with a natural metric resembling Thurston’s distance on Teichmuller space. The key feature is the notion of Manhattan curves, which allows us to interpolate between two isometric actions and produce plenty of bi-infinite geodesics in the space of metric structures. If time permits, I will talk about a higher-dimensional version of these curves, allowing us to find higher-dimensional manifolds in the space of metric structures. This is joint work with Stephen Cantrell and Cagri Sert.
Time: Friday, October 25th, 10 am (China Standard Time)
Venue:Zoom (virtual talk)
Zoom ID: 989 8689 0777 (Password: 864691)
Link: https://zoom.us/j/98986890777?pwd=bqbSH2abTPwqkzbDNr6E7YoH77gzXI.1
More information about the Geometric Group Theory Seminar can be found here
