Splittings of finitely generated groups over twoended subgroups
Author:
Brian H. Bowditch
Journal:
Trans. Amer. Math. Soc. 354 (2002), 10491078
MSC (2000):
Primary 20F65, 20E08
Published electronically:
October 26, 2001
MathSciNet review:
1867372
Fulltext PDF Free Access
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Abstract: We describe a means of constructing splittings of a oneended finitely generated group over twoended subgroups, starting with a finite collection of codimensionone twoended subgroups. In the case where all the twoended subgroups have twoended commensurators, we obtain an annulus theorem, and a form of the JSJ splitting of Rips and Sela. The construction uses ideas from the work of Dunwoody, Sageev and Swenson. We use a particular kind of order structure which combines cyclic orders and treelike structures. In the special case of hyperbolic groups, this provides a link between combinarorial constructions, and constructions arising from the topological structure of the boundary. In this context, we recover the annulus theorem of Scott and Swarup. We also show that a oneended finitely generated group which contains an infiniteorder element, and such that every infinite cyclic subgroup is (virtually) codimensionone is a virtual surface group.
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Additional Information
Brian H. Bowditch
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, Great Britain
DOI:
http://dx.doi.org/10.1090/S0002994701029075
PII:
S 00029947(01)029075
Received by editor(s):
January 31, 2001
Received by editor(s) in revised form:
July 1, 2001
Published electronically:
October 26, 2001
Article copyright:
© Copyright 2001 American Mathematical Society
