Algorithmic Solvability of the Lifting-Extension Problem

作者：Cadek Martin^*; Krcal Marek; Vokrinek Lukas

来源：Discrete & Computational Geometry, 2017, 57(4): 915-965.

DOI：10.1007/s00454-016-9855-6

• Homotopy classes
• Equivariant
• Fibrewise
• Lifting-extension problem
• Algorithmic computation
• Embeddability
• Moore-Postnikov tower

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 , for some , we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps ; the existence of such a map can be decided even for . This yields the first algorithm for deciding topological embeddability of a k-dimensional finite simplicial complex into under the condition . 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.

• 出版日期2017-6