Asian Journal of Mathematics

Volume 10 (2006)

Number 4

Modifying hyperkähler manifolds with circle symmetry

Pages: 815 – 826



Andrew S. Dancer (Jesus College, Oxford University, United Kingdom)

Andrew Swann


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.

Published 1 January 2006