| EPSRC Reference: |
EP/I028870/1 |
| Title: |
Low-dimensional topology and the complex of curves |
| Principal Investigator: |
Schleimer, Dr S |
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| Department: |
Mathematics |
| Organisation: |
University of Warwick |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
01 May 2011 |
Ends: |
30 April 2013 |
Value (£): |
88,321
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Topology in dimension three is the most accessible field ofmathematics; this is because three-dimensional space is the realm ofeveryday experience. Established by Poincare in a series of inspiringarticles in the late 1800's much of the work in low-dimensionaltopology was combinatorial in nature. In 1979 Thurston revolutionizedthe field by revealing deep connections to many other, more geometric,areas of mathematics.The geometric theme in low-dimensional topology has expanded to include coarse geometry. One striking success of this theme was the work of Masur and Minsky [1999, 2000]; they introduced the idea of using coarse geometry to understand the complex of curves. The complex of curves, defined by Harvey, is a combinatorial analogue of Teichmuller space.The novelty proposed here is to use the methods of Masur and Minsky tostudy and solve combinatorial problems, some first encountered byPoincare, in low-dimensional topology. The themes running through theproposal include handlebodies and Heegaard diagrams, the recognitionproblem for the three-sphere, the structure of the mapping classgroup, and the cobordism group of automorphisms of surfaces.
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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.warwick.ac.uk |