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.
KeywordsManifold Stratification Nite
Unable to display preview. Download preview PDF.
- [C]S. Chang, private communication.Google Scholar
- [D2]S. K. Donaldson, Gluing techniques in the cohomology of moduli spaces. Topological methods in modern mathematics (Stony Brook, NY, 1991), 137–170, Publish or Perish, Houston, TX, 1993.Google Scholar
- [GGK2]V. Ginzburg, V. Guillemin, Y. Karshon, Cobordism techniques in symplectic geometry, (in preparation.)Google Scholar
- [JW2]L. Jeffrey, J. Weitsman, Symplectic geometry of the moduli space of flat connections on a Riemann surface, inductive decompositions and vanishing theorems, preprint, December 1996, revised August 1997.Google Scholar
- [K]Y. Karshon, Moment maps and non-compact cobordisms, preprint (1997), dg-ga/9701006.Google Scholar
- [L2]K. Liu, Heat kernel and moduli spaces II, preprint, dg-ga/9612001.Google Scholar
- [MW1]E. Meinrenken, C. Woodward, Hom. Honian loop group actions and Verlinde factorization. To appear inJ. Diff. Geom. Google Scholar
- [MW2]E. Meinrenken, C. Woodward, Fusion of Hamiltonian loop group manifolds and cobordism. To appear inMath. Zeit. Google Scholar
- [Se]G. Segal, Lecture notes, Oxford, 1988.Google Scholar