Hypercontact structures and Floer homology

Hohloch, Sonja¹ ; Noetzel, Gregor² ; Salamon, Dietmar A³

¹ School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
² Mathematisches Institut, Universität Leipzig, Johannisgasse 26, 04103 Leipzig, Germany
³ Departement Mathematik, ETH Zentrum, Rämistrasse 101, CH-8092 Zürich, Switzerland

Geometry & topology, Tome 13 (2009) no. 5, pp. 2543-2617.

Résumé

We introduce a new Floer theory associated to a pair consisting of a Cartan hypercontact $3$–manifold $M$ and a hyperkähler 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.

Détail

DOI : 10.2140/gt.2009.13.2543

Keywords: Floer homology, hyperkaehler, hypercontact

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