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Rigorous length spectrum from approximate Dirichlet domain


Speaker: Maria Trnkova, UC Davis
Location: 2112 MSB
Start time: Mon, Feb 13 2017, 10:00AM

A computer program SnapPea constructs a length spectrum of a hyperbolic 3-manifold M using a algorithm described by Hodgson-Weeks. The algorithm uses tiling of the universal cover by translations of a Dirichlet domain of M by elements of a fundamental group. It does not use exact data but works surprisingly well in practice. In our talk we explain why an approximate Dirichlet domain can work equally well as an exact Dirichlet domain. We demonstrate an improvements in SnapPea's algorithm for rigorous construction of length spectrum of a hyperbolic 3-manifold. If time permit we show some applications of rigorous length spectra for Dehn parental test.