Fungible obstructions to embedding 2-complexes

2021/05/23 by Avramidi, Grigori, Phan, T. Tam Nguyen
#Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2105.10984

Abstract

We give examples of finite, simplicial 2-complexes that do not PL embed in ℝ⁴ and exhibit, for each such complex, a family of PL immersions into ℝ⁴ 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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