Melissa Liu (Part 3) M2U00124

Melissa Liu speaks at Northeastern university. Guest Speaker: Melissa Liu Columbia University Title: Moduli spaces of flat bundles over a nonorientable surface Date: Tuesday, November 18, 2008 Time: 1:00 p.m. Location: 509 Lake Hall In "The Yang-Mills equations over Riemann surfaces", Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the poing of view of Morse theory. Nan-Kuo Ho and I generalized their study to all closed, compact, connected, possibly nonorientable surfaces. I will review the work of Atiyah and Bott and describe my joint work with Ho. Let G be a compact Lie group, and let S a connected, closed, orientable or nonorientable surface. The moduli space of flat G-bundles over S can be identified with Hom(\pi_1(S), G)/G. When S is orientable, the G-equivariant Poincare series of the representation variety Hom(\pi_1(S),G) can be computed by the Atiyah-Bott recursion relations derived from the Morse stratification of the Yang-Mills functional. I will describe computations of the G-equivariant Poincare series of Hom(\pi_1(S), G) for a nonorientable surface S when G=U(2), SU(2), U(3), SU(3). Unlike the orientable case, the Morse stratification of the Yang-Mills functional is not perfect, and the real kirwan map is not surjective. This is a joint work with Nan-Kuo Ho.

Category:

Science & Technology

Tags:

• Moduli spaces
• flat bundles
• nonorientable surface