An obstruction to 3-dimensional thickenings
Francisco F. Lasheras · Proceedings of the American Mathematical Society · 1999
In this paper we give a characterization of those locally finite 2 2 -dimensional simplicial complexes that have an orientable 3 3 -manifold thickening. This leads to an obstruction for a fake surface X X to admit such a thickening. The obstruction is defined in H 1 ( Γ ; Z 2 ) H^1(\Gamma ;{\mathbf {Z}}_2) , where Γ ⊂ X \Gamma \subset X is the subgraph consisting of all the 1 1 -simplexes of order three.