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Open Quantum Systems Decoherence
Quantum Simulation
Identifying lens spaces in polynomial time
arXiv
Authors: Greg Kuperberg
Year
2015
Paper ID
27329
Status
Preprint
Abstract Read
~2 min
Abstract Words
77
Citations
N/A
Abstract
We show that if a closed, oriented 3-manifold M is promised to be homeomorphic to a lens space L(n,k) with n and k unknown, then we can compute both n and k in polynomial time in the size of the triangulation of M. The tricky part is the parameter k. The idea of the algorithm is to calculate Reidemeister torsion using numerical analysis over the complex numbers, rather than working directly in a cyclotomic field.
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- We show that if a closed, oriented 3-manifold M is promised to be homeomorphic to a lens space L(n,k) with n and k unknown, then we can compute both n and k in polynomial time...
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