Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: A universal Cannon-Thurston map and the surviving complex
Speaker: Chris Leininger, Rice University
Date: February 8, 2021
Time: 18:30:00 Hours
Venue: via Zoom
Abstract: The fundamental group of a surface (closed or with punctures) acts on the curve complex of the surface with one additional puncture via the Birman Exact Sequence. I will describe a construction of a continuous, equivariant map from a subset of the circle at infinity of the universal cover of the surface onto the Gromov boundary of the curve complex (along the way, explaining what these objects and actions are). This map is universal with respect to all Cannon-Thurston maps coming from type-preserving Kleinian representations without accidental parabolics. In the case of closed surfaces, this map was constructed in joint work with Mj and Schleimer, and in this talk I will talk about an extension to the case of punctured surfaces obtained in joint work with Gultepe and Pho-On. The proof for punctured surfaces involves constructing a continuous equivariant map to the Gromov boundary of a "larger" complex called the surviving complex. I will describe this complex, its Gromov boundary, and the construction of the map.
Title of Talk: A universal Cannon-Thurston map and the surviving complex
Speaker: Chris Leininger, Rice University
Date: February 8, 2021
Time: 18:30:00 Hours
Venue: via Zoom
Abstract: The fundamental group of a surface (closed or with punctures) acts on the curve complex of the surface with one additional puncture via the Birman Exact Sequence. I will describe a construction of a continuous, equivariant map from a subset of the circle at infinity of the universal cover of the surface onto the Gromov boundary of the curve complex (along the way, explaining what these objects and actions are). This map is universal with respect to all Cannon-Thurston maps coming from type-preserving Kleinian representations without accidental parabolics. In the case of closed surfaces, this map was constructed in joint work with Mj and Schleimer, and in this talk I will talk about an extension to the case of punctured surfaces obtained in joint work with Gultepe and Pho-On. The proof for punctured surfaces involves constructing a continuous equivariant map to the Gromov boundary of a "larger" complex called the surviving complex. I will describe this complex, its Gromov boundary, and the construction of the map.