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

Corson, J.; Trace, B.

doi:10.1090/S0002-9939-98-04158-6

The 6-property for simplicial complexes and a combinatorial Cartan-Hadamard theorem for manifolds
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by J. M. Corson and B. Trace PDF

Proc. Amer. Math. Soc. 126 (1998), 917-924 Request permission

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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