Algorithmic Solvability of the Lifting Extension Problem
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Discrete & Computational Geometry |
| MU Faculty or unit | |
| 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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