| EPSRC Reference: |
GR/S06462/01 |
| Title: |
Convergence actions on the 2-sphere and the weak hyperbolisation conjecture. |
| Principal Investigator: |
Niblo, Professor GA |
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| Department: |
School of Mathematics |
| Organisation: |
University of Southampton |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
30 July 2002 |
Ends: |
29 October 2002 |
Value (£): |
2,370
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Swenson has shown that given a closed non-Haken 3-manifold containing an immersed incompressible surfacer satisfying certain separation properties, there is a canonical action of the fundamental group on the 2-sphere. The longterm goal of this project is to generalise the result to sufficiently rich families of immersed incompressible surfaces and to complete it by showing that, with the right notion of sufficiently rich, the induced action on the 2-sphere is a unifom convergence action. It then follows from work of Bowditch that the fundamental group of the 3-manifold is word hyperbolic. This will establish the so-called weak hyperbolisation conjecture for a class of non-Haken 3-manifolds.The aim of this visit is to investigate the notion of sufficiently rich simplifying it as far as possible so as to begin toand to analyse the induced action on the 2-sphere.The prinicipal tools tobe used are an analysis of the CAT(0)cube complex associated to thefamily of surfaces (Niblo's area of expertise) and Swenson's work on the structure at infinity of CAT(0) spaces.
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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 |
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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.soton.ac.uk |