# Extendability of Continuous Maps Is Undecidable

@article{adek2014ExtendabilityOC,
title={Extendability of Continuous Maps Is Undecidable},
author={Martin {\vC}adek and Marek Krc{\'a}l and Jir{\'i} Matousek and Luk{\'a}s Vokr{\'i}nek and Uli Wagner},
journal={Discrete \& Computational Geometry},
year={2014},
volume={51},
pages={24-66}
}
• Published 10 February 2013
• Mathematics
• Discrete & Computational Geometry
We consider two basic problems of algebraic topology: the extension problem and the computation of higher homotopy groups, from the point of view of computability and computational complexity.The extension problem is the following: Given topological spaces X and Y, a subspace A⊆X, and a (continuous) map f:A→Y, decide whether f can be extended to a continuous map $\bar{f}\colon X\to Y$. All spaces are given as finite simplicial complexes, and the map f is simplicial.Recent positive algorithmic…
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