On the cut point conjecture
Author:
G. A. Swarup
Journal:
Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 98-100
MSC (1991):
Primary 20F32; Secondary 20J05, 57M40
DOI:
https://doi.org/10.1090/S1079-6762-96-00013-3
MathSciNet review:
1412948
Full-text PDF Free Access
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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.
- Mladen Bestvina and Mark Feighn, Bounding the complexity of simplicial group actions on trees, Invent. Math. 103 (1991), no. 3, 449–469. MR 1091614, DOI 10.1007/BF01239522
- Mladen Bestvina and Mark Feighn, Stable actions of groups on real trees, Invent. Math. 121 (1995), no. 2, 287–321. MR 1346208, DOI 10.1007/BF01884300
- Mladen Bestvina and Geoffrey Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), no. 3, 469–481. MR 1096169, DOI 10.1090/S0894-0347-1991-1096169-1
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- —, Boundaries of strongly accessible groups, Preprint (1996).
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- —, Cut points and canonical splittings of hyperbolic groups, Preprint (1995).
- W. Grosso, Unpublished manuscript, Berkeley (1995).
- G. Levitt, Nonnesting actions on real trees, Preprint (1996).
- G. P. Scott and G. A. Swarup, An algebraic annulus theorem, Preprint (1995).
- M. Bestvina and M. Feighn, Bounding the complexity of simplicial actions on trees, Inv. Math. 103 (1993), 449–469.
- —, Stable actions of groups on real trees, Inv. Math. 121 (1995), 287-361.
- M. Bestvina and G. Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4 (1991), 469–481.
- B. H. Bowditch, Treelike structures arising from continua and convergence groups, Preprint (1995).
- —, Boundaries of strongly accessible groups, Preprint (1996).
- —, Group actions on trees and dendrons, Preprint (1995).
- —, Cut points and canonical splittings of hyperbolic groups, Preprint (1995).
- W. Grosso, Unpublished manuscript, Berkeley (1995).
- G. Levitt, Nonnesting actions on real trees, Preprint (1996).
- 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
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 $60$th birthday
Communicated by:
Walter Neumann
Article copyright:
© Copyright 1996
American Mathematical Society
