Moduli Spaces of Flat Connections on 2-Manifolds, Cobordism, and Witten’s Volume Formulas
According to Atiyah-Bott [ABA] the moduli space of flat connections on a compact oriented 2-manifold with prescribed holonomies around the boundary is a finite-dimensional symplectic manifold, possibly singular. A standard approach [W1W2] to computing invariants (symplectic volumes, Riemann-Roch numbers, etc.) of the moduli space is to study the “factorization” of invariants under gluing of 2-manifolds along boundary components. Given such a factorization result, any choice of a “pants decomposition” of the 2-manifold reduces the computation of invariants to the three-holed sphere.
KeywordsModulus Space Conjugacy Class Boundary Component Symplectic Form Maximal Torus
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