Year: 2021
Type: preprint
Abstract: We give examples of finite, simplicial $2$-complexes that do not PL embed in $\mathbb{R}^4$ and exhibit, for each such complex, a family of PL immersions into $\mathbb{R}^4$ that hide the obstruction to embedding in "higher and higher order Milnor invariants". In addition, we show that the embedding obstructions defined by Krushkal in [8] vanish for our examples. We also answer a question in a paper of Avramidi-Okun-Schreve.
Source: arXiv (Cornell University)
Authors: Avramidi, Grigori, Phan, T. Tam Nguyen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3164874595