| EPSRC Reference: |
GR/M07281/01 |
| Title: |
NON-POSITIVE CURVATURE IN GROUP THEORY |
| Principal Investigator: |
Bridson, Professor M |
| Other Investigators: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 October 1998 |
Ends: |
30 September 2001 |
Value (£): |
118,032
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Much of the activity in geometric group theory in recent years has involved differing aspects of non-positive curvature. The three main classes of groups whose definitions encapsulate different facets of curvature are hyperbolic groups, (bi) automatic groups, and groups which act properly by isometries on CAT(0) spaces. The main purpose of the research programme presented here is to distinguish between these classes of groups. Working with Reeves, the proposed Research Fellow, I intend to draw all possible distinctions between these three classes of groups; the body of the proposal contains strategies for each case. I should stress that the objective is not to simply obtain examples by ad hoc means. Rather, each strategy, if successful, would also result in structural results of significant independent interest.I also propose, in partnership with Reeves, to continue to explore how encoding problems into the geometry of suitable non-positively curved spaces can be used as a tool for attacking questions in topology and group theory that a priori appear to have nothing to do with curvature.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ox.ac.uk |