Embedding obstructions and 4-dimensional thickenings of 2-complexes

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

2000-04-10

arxiv.org/abs/math/0004058v1

Mathematics

Geometric Topology

10 pages; To appear in Proc. Amer. Math. Soc

Scientific paper

The vanishing of Van Kampen's obstruction is known to be necessary and
sufficient for embeddability of a simplicial n-complex into $R^{2n}$ 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 $R^4$.

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