Extendability of simplicial maps is undecidable

Abstract

We present a short proof of the Čadek-Krčál-Matoušek-Vokřínek-Wagner result from the title (in the following form due to Filakovský-Wagner-Zhechev). For any fixed even $l$ there is no algorithm recognizing the extendability of the identity map of $S^l$ to a PL map $X\to S^l$ of given $2l$-dimensional simplicial complex $X$ containing a subdivision of $S^l$ as a given subcomplex. We also exhibit a gap in the Filakovský-Wagner-Zhechev proof that embeddability of complexes is undecidable in codimension $>1$.

10 pages, 1 figure, exposition improved, minor flaw corrected

References in corpus (2)

• Invariants of graph drawings in the plane
• Extendability of simplicial maps is undecidable

Cited by in corpus (2)

• Extendability of simplicial maps is undecidable
• Some `converses' to intrinsic linking theorems