Algorithmic aspects of immersibility and embeddability

Abstract

We analyze an algorithmic question about immersion theory: for which $m$, $n$, and $CAT=\mathbf{Diff}$ or $\mathbf{PL}$ is the question of whether an $m$-dimensional $CAT$-manifold is immersible in ${\mathbb{R}}^n$ decidable? As a corollary, we show that the smooth embeddability of an $m$-manifold with boundary in ${\mathbb{R}}^n$ is undecidable when $n-m$ is even and $11m\ge 10n+1$.

22 pages, 1 figure. New version includes additional minor clarifications in section 2

References in corpus (1)

• Quantitative null-cobordism