Algorithmic Solvability of the Lifting Extension Problem

• Autoři: ČADEK Martin; KRČÁL Marek; VOKŘÍNEK Lukáš
• Rok publikování: 2017
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Discrete & Computational Geometry
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://link.springer.com/article/10.1007%2Fs00454-016-9855-6
• Doi: http://dx.doi.org/10.1007/s00454-016-9855-6
• Obor: Obecná matematika
• Klíčová slova: homotopy classes ; equivariant ; fibrewise ; lifting-extension problem ; algorithmic computation; embeddability; Moore-Postnikov tower
• Popis: 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.

Související projekty

• Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku