The moduli space of flat connections on a principal G-bundle over a compact oriented surface of genus g greater than or equal to 1 is considered herein. Using the holonomies around noncontractible loops, the moduli space is described as a quotient of a submanifold of G(2g). An explicit expression is obtained for the symplectic form on the smooth part of moduli space, and several properties of this form are established.
机构:
Tohoku Univ, Grad Sch Informat Sci, Div Math, Sendai, Miyagi 9808579, JapanTohoku Univ, Grad Sch Informat Sci, Div Math, Sendai, Miyagi 9808579, Japan