Algorithmic solvability of the lifting extension problem

M. Čadek, M. Krcál, L. Vokřínek, Discrete & Computational Geometry 54 (2017) 915–965.


Journal Article | Published | English
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Abstract
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 dimX≤2d, for some d≥1, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps |X|→|Y|; the existence of such a map can be decided even for dimX≤2d+1. This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into Rn under the condition k≤23n−1. 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.
Publishing Year
Date Published
2017-06-01
Journal Title
Discrete & Computational Geometry
Volume
54
Issue
4
Page
915 - 965
ISSN
IST-REx-ID

Cite this

Čadek M, Krcál M, Vokřínek L. Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. 2017;54(4):915-965. doi:10.1007/s00454-016-9855-6
Čadek, M., Krcál, M., & Vokřínek, L. (2017). Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry, 54(4), 915–965. https://doi.org/10.1007/s00454-016-9855-6
Čadek, Martin, Marek Krcál, and Lukáš Vokřínek. “Algorithmic Solvability of the Lifting Extension Problem.” Discrete & Computational Geometry 54, no. 4 (2017): 915–65. https://doi.org/10.1007/s00454-016-9855-6.
M. Čadek, M. Krcál, and L. Vokřínek, “Algorithmic solvability of the lifting extension problem,” Discrete & Computational Geometry, vol. 54, no. 4, pp. 915–965, 2017.
Čadek M, Krcál M, Vokřínek L. 2017. Algorithmic solvability of the lifting extension problem. Discrete & Computational Geometry. 54(4), 915–965.
Čadek, Martin, et al. “Algorithmic Solvability of the Lifting Extension Problem.” Discrete & Computational Geometry, vol. 54, no. 4, Springer, 2017, pp. 915–65, doi:10.1007/s00454-016-9855-6.

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