Moduli Spaces of Flat Connections on 2-Manifolds, Cobordism, and Witten’s Volume Formulas

Abstract

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 SpaceConjugacy ClassBoundary ComponentSymplectic FormMaximal TorusThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.