Proceedings of the American Mathematical Society

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

Author(s): J. M. Corson; B. Trace
Journal: Proc. Amer. Math. Soc. 126 (1998), 917-924.
MSC (1991): Primary 57M20, 57N10, 20F06
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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

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

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