1. CJM Online first
|Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$-Betti Numbers|
Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's ``Yang-Mills over a Riemann Surface'' to compute $\mathbb Z/2$-Betti numbers of these spaces.
Keywords:cohomology of moduli spaces, holomorphic vector bundles
2. CJM 2005 (vol 57 pp. 871)
|Hermitian Yang-_Mills--Higgs Metrics on\\Complete KÃ¤hler Manifolds |
In this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact K\"ahler manifolds.
Keywords:vortex equation, Hermitian Yang--Mills--Higgs metric,, holomorphic vector bundle, KÃ¤hler manifolds