The Library
Peripheral splittings of groups
Tools
Tools
Tools
Bowditch, B. H. (2001) Peripheral splittings of groups. American Mathematical Society. Transactions, Vol.353 (No.10). pp. 4057-4082. doi:10.1090/S0002-9947-01-02835-5
![[img]](http://wrap.warwick.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
WRAP_Bowditch_peripheral_splittings.pdf - Requires a PDF viewer. Download (309Kb) |
|
PDF
WRAP_bowditch_coversheet.pdf - Requires a PDF viewer. Download (37Kb) |
Official URL: http://dx.doi.org/10.1090/S0002-9947-01-02835-5
Abstract
We define the notion of a "peripheral splitting" of a group. This
is essentially a representation of the group as the fundamental group of a bipartite
graph of groups, where all the vertex groups of one colour are held
fixed - the "peripheral subgroups". We develop the theory of such splittings
and prove an accessibility result. The theory mainly applies to relatively hyperbolic
groups with connected boundary, where the peripheral subgroups are
precisely the maximal parabolic subgroups. We show that if such a group admits
a non-trivial peripheral splitting, then its boundary has a global cut point.
Moreover, the non-peripheral vertex groups of such a splitting are themselves
relatively hyperbolic. These results, together with results from elsewhere, show
that under modest constraints on the peripheral subgroups, the boundary of
a relatively hyperbolic group is locally connected if it is connected. In retrospect,
one further deduces that the set of global cut points in such a boundary
has a simplicial treelike structure.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Hyperbolic groups, Maximal subgroups | ||||
| Journal or Publication Title: | American Mathematical Society. Transactions | ||||
| Publisher: | American Mathematical Society | ||||
| ISSN: | 0002-9947 | ||||
| Official Date: | 2001 | ||||
| Dates: |
|
||||
| Volume: | Vol.353 | ||||
| Number: | No.10 | ||||
| Page Range: | pp. 4057-4082 | ||||
| DOI: | 10.1090/S0002-9947-01-02835-5 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
