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The space of metric structures on hyperbolic groups
Geometry/Topology| Speaker: | Eduardo Oregon Reyes, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Thu, Nov 17 2022, 2:10PM |
Description
Hyperbolic groups are generalizations of finitely generated free groups
and surface groups, and they act properly and cocompactly by isometries
on Gromov hyperbolic spaces. For a fixed hyperbolic group, we can pack
all of its actions of this type into a single space, which extends the
classically studied Teichmüller and Outer spaces, but contains many more
interesting actions. I will talk about this space and some of its
properties when it is equipped with a natural metric that resembles
Thurston's Lipschitz distance on Teichmüller space. In particular, I
will explain how to find many bi-infinite geodesics in this space, which
I showed in joint work with Stephen Cantrell.