Algorithmic Solvability of the Lifting Extension Problem

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Authors

ČADEK Martin KRČÁL Marek VOKŘÍNEK Lukáš

Year of publication 2017
Type Article in Periodical
Magazine / Source Discrete & Computational Geometry
MU Faculty or unit

Faculty of Science

Citation
Web https://link.springer.com/article/10.1007%2Fs00454-016-9855-6
Doi http://dx.doi.org/10.1007/s00454-016-9855-6
Field General mathematics
Keywords homotopy classes ; equivariant ; fibrewise ; lifting-extension problem ; algorithmic computation; embeddability; Moore-Postnikov tower
Description Let X and Y be finite simplicial sets, both equipped with a free simplicial action of a finite group. Assuming that Y is d-connected and dimX less orequal to 2d, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps between geometric realizations of X and Y. This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into n-dimensional Euclidean space under certain conditions on k and n.
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