Identifying lens spaces in polynomial time
Geometric Topology
2018-03-16 v2 Quantum Physics
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.
Cite
@article{arxiv.1509.02887,
title = {Identifying lens spaces in polynomial time},
author = {Greg Kuperberg},
journal= {arXiv preprint arXiv:1509.02887},
year = {2018}
}
Comments
5 pages. A major revision with a new title, and with a classical algorithm rather than a quantum algorithm