31 citations · 45 across the 4 of their papers we have counts for
6 papers
Computing homotopy classes for diagrams
Marek Filakovský, Lukáš Vokřínek
We present an algorithm that, given finite simplicial sets , , with an action of a finite group , computes the set of homotopy classes of equivariant maps…
Are two given maps homotopic? An algorithmic viewpoint
Marek Filakovský, Lukáš Vokřínek
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 s…
Algorithmic solvability of the lifting-extension problem
Martin Čadek, Marek Krčál, Lukáš Vokřínek
Let and be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group . Assuming that is -connected…
Extendability of continuous maps is undecidable
Martin Cadek, Marek Krcal, Jiri Matousek +2
We consider two basic problems of algebraic topology, the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational…
Polynomial-time computation of homotopy groups and Postnikov systems in fixed dimension
Martin Cadek, Marek Krcal, Jiri Matousek +2
For several computational problems in homotopy theory, we obtain algorithms with running time polynomial in the input size. In particular, for every fixed k>1, there is a polynomia…
Computing all maps into a sphere
Martin Čadek, Marek Krčál, Jiří Matoušek +3
Given topological spaces X and Y, a fundamental problem of algebraic topology is understanding the structure of all continuous maps X -> Y . We consider a computational version, wh…