Algorithmic Solvability of the Lifting-Extension Problem

0479852 - ÚI 2018 US eng J - Journal Article
Čadek, M. - Krčál, Marek - Vokřínek, L.
Algorithmic Solvability of the Lifting-Extension Problem.
Discrete & Computational Geometry. Roč. 57, č. 4 (2017), s. 915-965. ISSN 0179-5376. E-ISSN 1432-0444
Keywords : postnikov systems * complexes * maps * Homotopy classes * Equivariant * Fibrewise * Lifting-extension problem * Algorithmic computation * Embeddability * Moore-Postnikov tower
Impact factor: 0.672, year: 2017

Let X and Y be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group G. Assuming that Y is d-connected and , for some , we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps ; the existence of such a map can be decided even for . This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into under the condition . More generally, we present an algorithm that, given a lifting-extension problem satisfying an appropriate stability assumption, computes the set of all homotopy classes of solutions. This result is new even in the non-equivariant situation.
Permanent Link: http://hdl.handle.net/11104/0275776