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Details of Grant 

EPSRC Reference: GR/R61048/01
Title: Non-compact representations of surface groups
Principal Investigator: Hitchin, Professor NJ
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematical Institute
Organisation: University of Oxford
Scheme: Standard Research (Pre-FEC)
Starts: 26 October 2001 Ends: 25 January 2002 Value (£): 5,180
EPSRC Research Topic Classifications:
Algebra & Geometry
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:  
Summary on Grant Application Form
The theory of Higgs Bundles and Morse Theory provides a meaning of determining in principle the topology of the space of representations of the fundamental group of a compact surface of genus> 1 into a non-compact lie group G. In practice, what is required is an understanding of the topology of the critical pointset of the Morse function, and this can be interpreted in the language of coherent systems. New developments in this theory have led to results for G = U(p,q). The theory of stable conic bundles should do the same for G = SP(2n,R).
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Organisation Website: http://www.ox.ac.uk