Group-valued implosion and parabolic structures

The purpose of this paper is twofold. First we extend the notion of symplectic implosion to the category of quasi-Hamiltonian K-manifolds, where K is a simply connected compact Lie group. The imploded cross-section of the double K × K turns out to be universal in a suitable sense. It is a singular space, but some of its strata have a nonsingular closure. This observation leads to interesting new examples of quasi-Hamiltonian K-manifolds, such as the "spinning 2n-sphere" for K = SU(n). Secondly we construct a universal ("master") moduli space of parabolic bundles with structure group K over a marked Riemann surface. The master moduli space carries a natural action of a maximal torus of K and a torus-invariant stratification into manifolds, each of which has a symplectic structure. An essential ingredient in the construction is the universal implosion. Paradoxically, although the universal implosion has no complex structure (it is the four-sphere for K = SU(2)), the master moduli space turns out to be a complex algebraic variety.