Asian Journal of Mathematics
Volume 10 (2006)
Modifying hyperkähler manifolds with circle symmetry
Pages: 815 – 826
A construction is introduced for modifying hyperkähler manifolds with tri-Hamiltonian circle action, that in favourable situations increases the second Betti number by one. This is based on the symplectic cut construction of Lerman. In 4 or 8 dimensions the construction may be interpreted as adding a D6-brane. A number of examples are given and a generalisation to three-Sasaki geometry discussed.
Hyperkähler manifold; three-Sasaki; symplectic cut; moment map; circle action
2010 Mathematics Subject Classification
Primary 53C26. Secondary 53D20, 57N65, 57S25.