Sum of Hamiltonian manifolds

Abstract

For any compact connected Lie group $G$, we study the Hamiltonian sum of two compact Hamiltonian group $G$-manifolds $(X^+,\omega^+,\mu^+)$ and $(X^-,\omega^-,\mu^-)$ with a common codimension 2 Hamiltonian submanifold $Z$ of the opposite equivariant Euler classes of the normal bundles. We establish that the symplectic reduction of the Hamiltonian sum agrees with the symplectic sum of the reduced symplectic manifolds. We also compare the equivariant first Chern class of the Hamiltonian sum with the equivariant first Chern classes of $X^\pm$.