Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

An obstruction to 3-dimensional thickenings

Author(s): Francisco F. Lasheras
Journal: Proc. Amer. Math. Soc. 128 (2000), 893-902.
MSC (2000): Primary 57M20; Secondary 57Q35
Posted: September 27, 1999
MathSciNet review: 1621973
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In this paper we give a characterization of those locally finite -dimensional simplicial complexes that have an orientable -manifold thickening. This leads to an obstruction for a fake surface 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 -simplexes of order three.

References:

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

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|