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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Hypercontact structures and Floer homology

Sonja Hohloch, Gregor Noetzel and Dietmar A Salamon

Geometry & Topology 13 (2009) 2543–2617
Abstract

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.

Keywords
Floer homology, hyperkaehler, hypercontact
Mathematical Subject Classification 2000
Primary: 53D40, 32Q15
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
Authors
Sonja Hohloch
School of Mathematical Sciences
Tel Aviv University
Ramat Aviv
Tel Aviv 69978
Israel
Gregor Noetzel
Mathematisches Institut
Universität Leipzig
Johannisgasse 26
04103 Leipzig
Germany
Dietmar A Salamon
Departement Mathematik
ETH Zentrum
Rämistrasse 101
CH-8092 Zürich
Switzerland