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

DOI:
https://doi.org/10.1090/S0002-9939-98-04158-6

MathSciNet review:
1425116

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Abstract | References | Similar Articles | Additional Information

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 -manifold has a 2-dimensional spine with the 6-property, then we show that the interior of is covered by euclidean -space. In dimension , 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:
https://doi.org/10.1090/S0002-9939-98-04158-6

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