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Modifying hyperkaehler manifolds with circle symmetry

Andrew Dancer·Andrew Swann
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Abstract

A construction is introduced for modifying hyperkaehler 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 generalisations to three-Sasaki and hypersymplectic geometry discussed.

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Andrew Dancer, Andrew Swann. 2005-10-25. Modifying hyperkaehler manifolds with circle symmetry. https://arxiv.org/abs/math/0510501

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