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Embedding obstructions and $4$-dimensional thickenings of $2$-complexes

Author: Vyacheslav S. Krushkal
Journal: Proc. Amer. Math. Soc. 128 (2000), 3683-3691
MSC (1991): Primary 57M20, 57Q35, 55S30, 57M25
Published electronically: May 18, 2000
MathSciNet review: 1690995
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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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Additional Information

Vyacheslav S. Krushkal
Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520

Received by editor(s): May 20, 1998
Received by editor(s) in revised form: January 29, 1999
Published electronically: May 18, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society