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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The 6-property for simplicial complexes
and a combinatorial Cartan-Hadamard theorem
for manifolds


Authors: J. M. Corson and B. Trace
Journal: Proc. Amer. Math. Soc. 126 (1998), 917-924
MSC (1991): Primary 57M20, 57N10, 20F06
MathSciNet review: 1425116
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Abstract: The 6-property for 2-dimensional simplicial complexes is the condition that every nontrivial circuit in the link of a vertex has length greater than or equal to six. If a compact $n$-manifold $M$ has a 2-dimensional spine with the 6-property, then we show that the interior of $M$ is covered by euclidean $n$-space. In dimension $n=3$, we show further that such a 3-manifold is Haken.


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Additional Information

J. M. Corson
Affiliation: Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
Email: jcorson@mathdept.as.ua.edu

B. Trace
Affiliation: Department of Mathematics, University of Alabama, Box 870350, Tuscaloosa, Alabama 35487-0350
Email: btrace@mathdept.as.ua.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04158-6
PII: S 0002-9939(98)04158-6
Keywords: Manifold, spine, universal cover, 6-property, collapsing
Received by editor(s): March 26, 1996
Received by editor(s) in revised form: September 3, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society