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December 2006 Modifying hyperkähler manifolds with circle symmetry
Andrew Dancer, Andrew Swann
Asian J. Math. 10(4): 815-826 (December 2006).


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.


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Andrew Dancer. Andrew Swann. "Modifying hyperkähler manifolds with circle symmetry." Asian J. Math. 10 (4) 815 - 826, December 2006.


Published: December 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1156.53313
MathSciNet: MR2279158

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

Keywords: circle action , Hyperkähler manifold , moment map , symplectic cut , three-Sasaki

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 4 • December 2006
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