Group-valued Implosion and Parabolic Structures
| dc.creator | Hurtubise, Jacques | |
| dc.creator | Jeffrey, Lisa | |
| dc.creator | Sjamaar, Reyer | |
| dc.date | 2004-02-27 | |
| dc.date.accessioned | 2026-07-07T06:30:20Z | |
| dc.date.available | 2026-07-07T06:30:20Z | |
| dc.description | 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 $K\times K$ 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. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402464 | |
| dc.identifier | http://arxiv.org/abs/math/0402464 | |
| dc.identifier | Amer. J. Math. 128 (2006), no. 1, 167--214 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98316 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53D20; 53D30 | |
| dc.title | Group-valued Implosion and Parabolic Structures | |
| dc.type | text |