Are two given maps homotopic? An algorithmic viewpoint
Algebraic Topology
2013-12-10 v1 Computational Geometry
Abstract
This paper presents two algorithms. In their simplest form, the first algorithm decides the existence of a pointed homotopy between given simplicial maps f, g from X to Y and the second computes the group of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected and the algorithms run in polynomial time when the dimension of X is fixed. More generally, these algorithms work relative to a subspace A of X, fibrewise over a simply connected B and also equivariantly when all spaces are equipped with a free action of a fixed finite group G.
Cite
@article{arxiv.1312.2337,
title = {Are two given maps homotopic? An algorithmic viewpoint},
author = {Marek Filakovský and Lukáš Vokřínek},
journal= {arXiv preprint arXiv:1312.2337},
year = {2013}
}