2013/12/09 by Marek Filakovský, Filakovský, Marek, Lukáš Vokřínek +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Primary 55Q05 #Secondary 55P40 #cs.CG #math.AT #msc:55P40 #msc:55Q05
paper · pdf · doi:10.48550/arxiv.1312.2337
arxiv created 2013/12/09 · arxiv updated 2013/12/10
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 [ΣX,Y]^* 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.