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Nan-Kuo Ho 
2010-03-23 
09:00 - 10:00 
308 , Mathematics Research Center Building (ori. New Math. Bldg.)

Atiyah and Bott studied the moduli space of °at connections over a Rie- mann surface from a Morse theory point of view via the use of Yang-Mills functional. They showed that the Morse strati¯cation of the space of all connections over a Riemann surface is gauge-equivariantly perfect and con- cluded recursive formulas for the equivariant Poincar¶e series of the space of °at connections over a Riemann surface. We extend their Morse theory approach to study the moduli space of °at connections over a nonorientable surface. Contrary to equivariant perfection of the strati¯cation in Atiyah-Bott's study, the di®erence of the equivariant Morse series and the equivariant Poincar¶e series doesn't necessarily achieve the minimal possible value 0 here. We introduce the notion of antiperfec- tion and explain how equivariant antiperfection of the Morse strati¯cation derives the gauge-equivariant Poincar¶e series of the space of °at connections over a nonorientable surface in certain cases. This is a joint work with Chiu-Chu Melissa Liu.