1. CMB 2000 (vol 43 pp. 183)
|A Gauge Theoretic Proof of the Abel-Jacobi Theorem |
We present a new, simple proof of the classical Abel-Jacobi theorem using some elementary gauge theoretic arguments.
Keywords:Abel-Jacobi theorem, abelian gauge theory
2. CMB 1997 (vol 40 pp. 285)
|The space of harmonic maps from the $2$-sphere to the complex projective plane |
In this paper we study the topology of the space of harmonic maps from $S^2$ to $\CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for the space of harmonic maps to $\CP n$ for $n\geq 2$. We show that the components of maps to $\CP 2$ are complex manifolds.