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An obstruction to 3-dimensional thickenings

Author: Francisco F. Lasheras
Journal: Proc. Amer. Math. Soc. 128 (2000), 893-902
MSC (2000): Primary 57M20; Secondary 57Q35
Published electronically: September 27, 1999
MathSciNet review: 1621973
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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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Additional Information

Francisco F. Lasheras
Affiliation: Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain

Received by editor(s): October 27, 1997
Received by editor(s) in revised form: April 17, 1998
Published electronically: September 27, 1999
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society