Fungible obstructions to embedding 2-complexes

Grigori Avramidi; T. Tam Nguyen Phan

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arXiv · 2105.10984

Fungible obstructions to embedding 2-complexes

Grigori Avramidi·T. Tam Nguyen Phan

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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.

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BibTeX RIS

Grigori Avramidi, T. Tam Nguyen Phan. 2021-05-23. Fungible obstructions to embedding 2-complexes. https://arxiv.org/abs/2105.10984

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