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On the cut point conjecture
Author(s):
G.
A.
Swarup
Journal:
Electron. Res. Announc. Amer. Math. Soc.
2
(1996),
98-100.
MSC (1991):
Primary 20F32;
Secondary 20J05, 57M40
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Abstract:
We sketch a proof of the fact that the Gromov boundary of a hyperbolic group does not have a global cut point if it is connected. This implies, by a theorem of Bestvina and Mess, that the boundary is locally connected if it is connected.
References:
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- M. Bestvina and M. Feighn, Bounding the complexity of simplicial actions on trees, Inv. Math. 103 (1993), 449--469. MR 92c:20044
- 2.
- ------, Stable actions of groups on real trees, Inv. Math. 121 (1995), 287-361. MR 96h:20056
- 3.
- M. Bestvina and G. Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), 469--481. MR 93j:20076
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- B. H. Bowditch, Treelike structures arising from continua and convergence groups, Preprint (1995).
- 5.
- ------, Boundaries of strongly accessible groups, Preprint (1996).
- 6.
- ------, Group actions on trees and dendrons, Preprint (1995).
- 7.
- ------, Cut points and canonical splittings of hyperbolic groups, Preprint (1995).
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- W. Grosso, Unpublished manuscript, Berkeley (1995).
- 9.
- G. Levitt, Nonnesting actions on real trees, Preprint (1996).
- 10.
- G. P. Scott and G. A. Swarup, An algebraic annulus theorem, Preprint (1995).
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Additional Information:
G.
A.
Swarup
Affiliation:
The University of Melbourne, Parkville, 3052, Victoria, Australia
DOI:
10.1090/S1079-6762-96-00013-3
PII:
S 1079-6762(96)00013-3
Keywords:
Gromov hyperbolic group,
Gromov boundary,
cut point,
local connectedness,
dendrite,
R-tree
Received by editor(s):
June 4, 1996
Dedicated:
Dedicated to John Stallings on his 60th birthday
Communicated by:
Walter Neumann
Copyright of article:
Copyright
1996,
American Mathematical Society
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