Seminar:
Group Actions, Geometry and Dynamics
Event time:
Monday, September 19, 2022 - 4:00pm
Location:
LOM 206
Speaker:
Hee Oh
Speaker affiliation:
Yale
Event description:
For a convex cocompact Kleinian group Γ<SO(n,1), Sullivan (around 1985) established a fundamental relation among the critical exponent, the bottom of the L^2-spectrum of the hyperbolic manifold Γ∖Hn, the quasi-regular representation L2(Γ∖G) and the Hausdorff dimension of the limit set. We consider a higher rank analogue of this relation. For self-joinings of convex cocompact Kleinian groups (or more generally for any Anosov subgroup of a product of rank one simple algebraic groups), we discover a surprising fact that they satisfy a similar relation as convex cocompact groups with “small” critical exponents.
This talk is based on joint works with Dongryul Kim and Yair Minsky, and with Sam Edwards in different parts.