Embedding obstructions and 4-dimensional thickenings of 2-complexes

Krushkal, Vyacheslav

doi:10.1090/S0002-9939-00-05458-7

Embedding obstructions and 4-dimensional thickenings of 2-complexes
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by Vyacheslav S. Krushkal

Proc. Amer. Math. Soc. 128 (2000), 3683-3691

DOI: https://doi.org/10.1090/S0002-9939-00-05458-7

Published electronically: May 18, 2000

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Abstract:

The vanishing of Van Kampen’s obstruction is known to be necessary and sufficient for embeddability of a simplicial $n$-complex into ${\mathbb {R}}^{2n}$ for $n\neq 2$, and it was recently shown to be incomplete for $n=2$. We use algebraic-topological invariants of four-manifolds with boundary to introduce a sequence of higher embedding obstructions for a class of $2$-complexes in ${\mathbb {R}}^4$.

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