Geodesic
Identifying lens spaces in polynomial time
Kuperberg, Greg1
1 Department of Mathematics, University of California, Davis, CA, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 767-778

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2018.18.767
Classification : 57M27, 65G30, 68Q15, 68W01
Keywords: 3–manifolds, lens spaces, Reidemeister torsion

Kuperberg, Greg 1

1 Department of Mathematics, University of California, Davis, CA, United States 
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Kuperberg, Greg. Identifying lens spaces in polynomial time. Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 767-778. doi: 10.2140/agt.2018.18.767

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