<pre>In the first part of this thesis we show that, for a given non-arithmetic closed hyperbolic <i>$</i><i>n</i><i>$</i> manifold <i>$</i><i>M</i><i>$</i>, there exist for each positive integer <i>$</i><i>j</i><i>$</i>, a set <i>$</i><i>M_</i><i>1</i><i>,...,M_j</i><i>$</i> of pairwise nonisometric, strongly isospectral, finite covers of <i>$</i><i>M</i><i>$</i>, and such that for each <i>$</i><i>i,i'</i><i>$</i> one has isomorphisms of cohomology groups <i>$</i><i>H^*(M_i,</i><i>\Zbb</i><i>)=H^*(M_{i'},</i><i>\Zbb</i><i>)</i><i>$</i> which are compatible with respect to the natural maps induced by the cover. In the second part, we prove that hyperbolic <i>$</i><i>2</i><i>$</i>- and <i>$</i><i>3</i><i>$</i>-manifolds which arise from principal congruence subgroups of a maixmal order in a quaternion algebra having type number <i>$</i><i>1</i><i>$</i> 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.</pre>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/23803548 |
| Date | 31 July 2023 |
| Creators | Justin E Katz (16707999) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Spectral_Rigidity_and_Flexibility_of_Hyperbolic_Manifolds/23803548 |
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