Identifying lens spaces in polynomial time

Kuperberg, Greg

doi:10.2140/agt.2018.18.767

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Identifying lens spaces in polynomial time

Greg Kuperberg

Algebraic & Geometric Topology 18 (2018) 767–778

DOI: 10.2140/agt.2018.18.767

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.

Keywords

3–manifolds, lens spaces, Reidemeister torsion

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 65G30, 68Q15, 68W01

References

Publication

Received: 26 April 2016

Revised: 31 December 2017

Accepted: 25 January 2018

Published: 12 March 2018

Authors

Greg Kuperberg
Department of Mathematics University of California Davis, CA United States

Volume 18, issue 2 (2018)