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Boundary and lens rigidity of finite quotients

Authors:	Christopher Croke

Institution:	Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395

Abstract:	We consider compact Riemannian manifolds $(M,\partial M,g)$ with boundary $\partial M$ and metric on which a finite group $\Gamma$ acts freely. We determine the extent to which certain rigidity properties of $(M,\partial M,g)$ descend to the quotient $(M/\Gamma,\partial/\Gamma,g)$ . In particular, we show by example that if $(M,\partial M,g)$ is boundary rigid, then $(M/\Gamma,\partial/\Gamma,g)$ need not be. On the other hand, lens rigidity of $(M,\partial M,g)$ does pass to the quotient.

Keywords:	Boundary rigidity lens rigidity quotients

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