Extendability of Continuous Maps Is Undecidable

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Authors

ČADEK Martin KRČÁL Marek MATOUŠEK Jiří VOKŘÍNEK Lukáš WAGNER Uli

Year of publication 2014
Type Article in Periodical
Magazine / Source Discrete & Computational Geometry
MU Faculty or unit

Faculty of Science

Citation
Web http://link.springer.com/article/10.1007/s00454-013-9551-8/fulltext.html
Doi http://dx.doi.org/10.1007/s00454-013-9551-8
Field General mathematics
Keywords extension problem ; homotopy group; undecidability; hardness
Description Given topological spaces X and Y, a subspace A of X, and a continuous map f from A to Y, decide whether f can be extended to a continuous map F from X to Y. All spaces are given as finite simplicial complexes, and the map f is simplicial. The paper shows that for dimX=2k, the extension problem with (k minus 1) connected Y becomes undecidable.
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