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Hypercontact structures
and Floer homology
Sonja Hohloch, Gregor Noetzel and Dietmar A Salamon |
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Geometry & Topology 13 (2009) 2543–2617
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Abstract |
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We introduce a new Floer theory associated to a pair consisting of a Cartan hypercontact –manifold and a hyperkähler manifold . The theory is a based on the gradient flow of the hypersymplectic action functional on the space of maps from to . The gradient flow lines satisfy a nonlinear analogue of the Dirac equation. We work out the details of the analysis and compute the Floer homology groups in the case where is flat. As a corollary we derive an existence theorem for the –dimensional perturbed nonlinear Dirac equation. |
Keywords
Floer homology, hyperkaehler, hypercontact
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Mathematical Subject Classification 2000
Primary: 53D40, 32Q15
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References |
Publication
Received: 24 October 2008
Revised: 15 April 2009
Accepted: 25 June 2009
Published: 21 July 2009
Proposed: Simon Donaldson
Seconded: Leonid Polterovich, Yasha Eliashberg
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Authors |
| Sonja Hohloch | |
| School of Mathematical
Sciences Tel Aviv University Ramat Aviv Tel Aviv 69978 Israel |
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| Gregor Noetzel | |
| Mathematisches Institut Universität Leipzig Johannisgasse 26 04103 Leipzig Germany |
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| Dietmar A Salamon | |
| Departement Mathematik ETH Zentrum Rämistrasse 101 CH-8092 Zürich Switzerland |
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