Monday, Geometry and Topology Seminar, 12 NOV, Emily Stark. Title “Boundary maps in non-positive curvature”
Geometry & Topology Seminar
Speaker: Emily Stark(Technion)
Topic: Boundary maps in non-positive curvature
Place: room 614 in the Science & Education Building
Date: Monday, November 12, 2018
Seminal work of Cannon and Thurston in the 1980s proved if M is a fibered hyperbolic 3-manifold, then there exists a surjection from the boundary of the universal cover of the surface fiber to the boundary of the universal cover of the 3-manifold that continuously extends the inclusion between these universal covers. In fact, their theorem provides a naturally-occuring continuous finite-to-one map from the circle onto the 2-sphere. Gromov proved every hyperbolic group has a boundary that is well-defined up to homeomorphism, hence one can study “Cannon–Thurston maps” in a more general context. Mitra (Mj) extended the work of Cannon and Thurston to prove such boundary maps exist for any normal hyperbolic subgroup of a hyperbolic group. I will explain why a similar theorem fails for certain CAT(0) groups. This is joint work with Beeker–Cordes–Gardam–Gupta.