A triple-point Whitney trick

Abstract

We use a triple-point version of the Whitney trick to show that ornaments of three orientable $(2k-1)$-manifolds in ${\mathbb{R}}^{3k-1}$, $k>2$, are classified by the $\mu$-invariant. A very similar (but not identical) construction was found independently by I. Mabillard and U. Wagner, who also made it work in a much more general situation and obtained impressive applications. The present note is, by contrast, focused on a minimal working case of the construction.

5 pages. This paper is a more detailed exposition of 1.5 pages (Theorem 1.1 on pages 6-8) from arXiv:1711.03530v1