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
Full-text PDF Free Access
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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-cells is an open 
for universal covering spaces of closed 
-manifolds, J. Differential Geom. 35 (1992), 103-130. 
, Internat. J. Algebra Comput. 1 (1991), 395-406. Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M20, 57N10, 20F06
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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