English

Fungible obstructions to embedding 2-complexes

Geometric Topology 2021-08-04 v2 Combinatorics Group Theory

Abstract

We give examples of finite, simplicial 22-complexes that do not PL embed in R4\mathbb{R}^4 and exhibit, for each such complex, a family of PL immersions into R4\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.

Keywords

Cite

@article{arxiv.2105.10984,
  title  = {Fungible obstructions to embedding 2-complexes},
  author = {Grigori Avramidi and T. Tam Nguyen Phan},
  journal= {arXiv preprint arXiv:2105.10984},
  year   = {2021}
}

Comments

New in this version: we show that the embedding obstructions defined by Krushkal in [8] vanish for our examples. 21 pages, 12 figures

R2 v1 2026-06-24T02:23:17.580Z