Title
Hypercontact structures and Floer homology
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Geometry and topology. - -
Volume/pages
13(2009) , p. 2543-2617
ISSN
1364-0380
ISI
000268177200001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We introduce a new Floer theory associated to a pair consisting of a Cartan hypercontact 3-manifold M and a hyperkahler manifold X. The theory is a based on the gradient flow of the hypersymplectic action functional on the space of maps from M to X. 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 X is flat. As a corollary we derive an existence theorem for the 3-dimensional perturbed nonlinear Dirac equation.
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