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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
DOI: https://doi.org/10.1090/S0002-9939-99-05023-6
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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  • 1. J.M. Corson, B. Trace, ``Geometry and algebra of nonspherical $2$-complexes". J. London Math. Soc. 54(1996), 180-198. MR 98b:57007
  • 2. R. Geoghegan, ``Topological methods in group theory''. Book in preparation.
  • 3. C. Hog-Angeloni, W. Metzler, ``Geometric aspects of two-dimensional complexes'', pp. 1-50 of Two-dimensional Homotopy and Combinatorial Group Theory (C. Hog-Angeloni, W. Metzler, A.J. Sieradski ed.). Lecture Notes Series 197. London Math. Soc. Cambridge Univ. Press(1993). CMP 94:13
  • 4. H. Ikeda, ``Acyclic fake surfaces''. Topology 10(1971), 9-36. MR 48:5078
  • 5. W.S. Massey, ``Homology and Cohomology Theory". Marcel Dekker(1978). MR 58:7594
  • 6. L. Neuwirth, ``An algorithm for the construction of $3$-manifolds from $2$-complexes". Proc. Camb. Phil. Soc 64(1968), 603-613. MR 37:2231
  • 7. F. Quinn, ``Presentations and $2$-complexes, fake surfaces and singular $3$-manifolds". Virginia Polytechnic Institute. Blackburg Va.(1981). Preprint.
  • 8. C.P. Rourke, B.J. Sanderson, ``Introduction to Piecewise-Linear Topology". Springer(1972). MR 50:3236
  • 9. P. Wright, ``Formal $3$-deformations of $2$-polyhedra''. Proc. American Math. Soc. 37(1973), 305-308. MR 48:9730
  • 10. P. Wright, ``Covering $2$-dimensional polyhedra by $3$-manifold spines''. Topology 16(1977), 435-439. MR 56:16611

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Additional Information

Francisco F. Lasheras
Affiliation: Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain
Email: fjfer@cica.es

DOI: https://doi.org/10.1090/S0002-9939-99-05023-6
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

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