Spectral Rigidity and Flexibility of Hyperbolic Manifolds
Abstract
In the first part of this thesis we show that, for a given non-arithmetic closed hyperbolic n manifold M, there exist for each positive integer j, a set M1, ..., Mj of pairwise nonisometric, strongly isospectral, finite covers of M, and such that for each i, i0 one has isomorphisms of cohomology groups H∗ (Mi , Z) = H∗ (Mi ,Z) which are compatible with respect to the natural maps induced by the cover. In the second part, we prove that hyperbolic 2- and 3-manifolds which arise from principal congruence subgroups of a maixmal order in a quaternion algebra having type number 1 are absolutely spectrally rigid. One consequence of this is a partial answer to an outstanding question of Alan Reid, concerning the spectral rigidity of Hurwitz surfaces.
Degree
Ph.D.
Advisors
Shahidi, Purdue University.
Subject Area
Mathematics
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.