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SUMMARY:Morse theory and the moduli space of flat connections over a nonor
 ientable surface - Nan-Kuo\, H (National Tsing-Hua )
DTSTART:20110308T100000Z
DTEND:20110308T110000Z
UID:TALK30179@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We studied the moduli space of flat connections over a nonorie
 ntable surface via a Morse theory approach adapted from Atiyah and Bott's 
 work. We defined a Yang-Mills functional on the space of all connections o
 ver a nonorientable surface and obtained a Morse stratification of the spa
 ce. We defined "super central extension" of the fundamental group of the s
 urface. The representation varieties defined using super central extension
  correspond to gauge equivariant Yang-Mills connections and enable us to o
 btain reduction formulas for equivariant strata. To describe the phenomeno
 n of the stratification here\, we defined "anti-perfect Morse stratificati
 on"\, which is the case when the discrepancy (i.e. the difference between 
 Morse series and Poincare series) reaches its maximal possible value while
  the perfect Morse stratification is when the discrepancy reaches its mini
 mal possible value zero.\n\nThis is a joint work with Chiu-Chu Melissa Liu
 .\n\n
LOCATION:Seminar Room 1\, Newton Institute
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