Asian Journal of Mathematics

Volume 10 (2006)

Number 4

Modifying hyperkähler manifolds with circle symmetry

Pages: 815 – 826

DOI: http://dx.doi.org/10.4310/AJM.2006.v10.n4.a11

Authors

Andrew Dancer

Andrew Swann

Abstract

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.

Keywords

Hyperkähler manifold; three-Sasaki; symplectic cut; moment map; circle action

2010 Mathematics Subject Classification

Primary 53C26. Secondary 53D20, 57N65, 57S25.

Full Text (PDF format)