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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/9553

Title: Group-valued implosion and parabolic structures
Authors: Jeffrey, L.
Hurtubise, J.
Sjamaar, R.
Keywords: bundles
surfaces
moduli
spaces
Issue Date: 2006
Publisher: The Johns Hopkins University Press
Citation: Hurtubise, J., Jeffrey, L., & Sjamaar, R. (2006). Group-valued implosion and parabolic structures. American Journal of Mathematics, 128(1), 167-214.
Abstract: The purpose of this paper is twofold. First we extend the notion of symplectic implosion to the category of quasi-Hamiltonian an K-manifolds, where K is a simply connected compact Lie group. The imploded cross-section of the double K x 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.
Description: This article appeared in the American Journal of Mathematics, Volume 128, Issue 1, 2006, pages 167-214, Copyright © The Johns Hopkins University Press
URI: http://hdl.handle.net/1807/9553
ISSN: 0002-9327
Appears in Collections:Mathematics

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