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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
Full-text PDF Free Access
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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  -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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- S. G. Brick and M. L. Mihalik, The qsf property for groups and spaces, Math. Z. 220 (1995), 207-217. MR 96i:57009
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- M. Brown, The monotone union of open
 -cells is an open -cell, Proc. Amer. Math. Soc. 12 (1961), 812-814. MR 23:A4129
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- J. Corson and B. Trace, Geometry and algebra of nonspherical 2-complexes, J. London Math. Soc. 54 (1996), 180-198. CMP 96:14
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- M. W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983), 293-324. MR 86d:57025
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- R. C. Lyndon and P. E. Schupp, Combinatorial group theory, Ergeb. Math., Bd. 89, Springer, New York, 1977. MR 58:28182
- [MT]
- M. L. Mihalik and S. T. Tschantz, Tame combings of groups, Trans. Amer. Math. Soc. (to appear). CMP 96:12
- [P]
- V. Poénaru, Almost convex groups, Lipschitz combing, and
 for universal covering spaces of closed  -manifolds, J. Differential Geom. 35 (1992), 103-130. MR 93d:57032
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- J. Stallings and S. M. Gersten, Casson's idea about -manifolds whose universal cover is
 , Internat. J. Algebra Comput. 1 (1991), 395-406. MR 93b:57018
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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
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