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D. B. McReynolds

Publications and source records attributed to D. B. McReynolds.

41 records · Page 3Linked to original sources
arXiv2006

Length and eigenvalue equivalence

Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent when the sets of lengths of their (primitive) closed geodesics are equal. We give a general construction of eigenvalue equivalent and primitive length equivalent Riemannian manifolds. For example we show that every finite volume hyperbolic $n$--manifold has pairs of eigenvalue equivalent finite covers of arbitrarily large volume ratio. We also show the analogous result for primitive length equivalence.

math.GT↗
arXiv2006

Cusps of arithmetic orbifolds

This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a new subgroup separability result for general arithmetic lattices.

math.GT↗
arXiv2004

Peripheral separability and cusps of arithmetic hyperbolic orbifolds

For X = R, C, or H it is well known that cusp cross-sections of finite volume X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds modelled on the (2n+1)-dimensional Heisenberg group N_{2n+1} or the (4n+3)-dimensional quaternionic Heisenberg group N_{4n+3}(H). We give a necessary and sufficient condition for such manifolds to be diffeomorphic to a cusp cross-section of an arithmetic X-hyperbolic (n+1)-orbifold. A principal tool in the proof of this classification theorem is a subgroup separability result which may be of independent interest.

math.GT↗