An obstruction to 3-dimensional thickenings

Lasheras, Francisco

doi:10.1090/S0002-9939-99-05023-6

An obstruction to 3-dimensional thickenings
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by Francisco F. Lasheras PDF

Proc. Amer. Math. Soc. 128 (2000), 893-902 Request permission

Abstract:

In this paper we give a characterization of those locally finite $2$-dimensional simplicial complexes that have an orientable $3$-manifold thickening. This leads to an obstruction for a fake surface $X$ to admit such a thickening. The obstruction is defined in $H^1(\Gamma ;{\mathbf {Z}}_2)$, where $\Gamma \subset X$ is the subgraph consisting of all the $1$-simplexes of order three.

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