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2018 Identifying lens spaces in polynomial time
Greg Kuperberg
Algebr. Geom. Topol. 18(2): 767-778 (2018). 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.

Citation

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Greg Kuperberg. "Identifying lens spaces in polynomial time." Algebr. Geom. Topol. 18 (2) 767 - 778, 2018. https://doi.org/10.2140/agt.2018.18.767

Information

Received: 26 April 2016; Revised: 31 December 2017; Accepted: 25 January 2018; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859603
MathSciNet: MR3773737
Digital Object Identifier: 10.2140/agt.2018.18.767

Subjects:
Primary: 57M27
Secondary: 65G30, 68Q15, 68W01

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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