| EPSRC Reference: |
GR/M98159/01 |
| Title: |
MORSE THEORY OF CIRCLE-VALUED FUNCTIONS |
| Principal Investigator: |
Hitchin, Professor NJ |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Mathematical Institute |
| Organisation: |
University of Oxford |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
02 November 1999 |
Ends: |
01 January 2000 |
Value (£): |
3,500
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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The VF has a number of achievements to his credit in adapting analytical and topological approaches to Morse theory to the case when the Morse function takes values in a circle. This situation occurs in many places, notable where symplectic group actions do not have a moment map and in an infinite dimensional context in Floer theory. There are areas on the interface between physics and geometry where such techniques may well be useful. One of these lies in the deformation theory of special Lagrangian submanifolds of a Calabi-Yau maniforld, which is fundamental in the Strominger-Yau-Zaslow approach to mirror symmetry. Here deformations are governed by harmonic 1-forms on the submanifold and so intersection properties of nearby submanifolds depend on the zeros of closed 1-forms with periods, which can be thought of in terms of circle valued Morse functions. Also the S-duality conjectures for monopole moduli spaces concern harmonic forms with local coefficient systems and a Morse-theoretic viewpoint may shed some light on these.
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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 |