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Computing arithmetic invariants of 3-manifolds. (English) Zbl 1002.57044

Summary: Snap is a computer program for computing arithmetic invariants of hyperbolic 3-manifolds, built on Jeff Weeks’s SnapPea and the number theory package Pari. Its approach is to compute the hyperbolic structure to very high precision, and use this to find an exact description of the structure. Then the correctness of the hyperbolic structure can be verified, and the arithmetic invariants of Neumann and Reid can be computed. Snap also computes high precision numerical invariants such as volume, Chern-Simons invariant, eta invariant and the Borel regulator.

MathOverflow Questions:

Quadratic cusp shape

MSC:

57M50 General geometric structures on low-dimensional manifolds
57-04 Software, source code, etc. for problems pertaining to manifolds and cell complexes
57N10 Topology of general \(3\)-manifolds (MSC2010)

Software:

PARI/GP; SnapPea; Snap
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References:

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