Fredholm theory and transversality for noncompact pseudoholomorphic mapsin symplectizations

2004/03/19 by Dragomir L. Dragnev, Dragomir Dragnev · 12 citations
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.1002/cpa.20018

Abstract

Abstract We study pseudoholomorphic maps from a punctured Riemann surface into the symplectization of a contact manifold. A Fredholm theory yields the virtual dimension of the moduli spaces of such maps in terms of the Euler characteristic of the Riemann surface and the asymptotics data given by the periodic solutions of the Reeb vector field associated to the contact form. The transversality results establish the existence of additional structure for these spaces. To be more precise, we prove that these spaces are generically smooth manifolds, and therefore their virtual dimension coincides with their actual dimension. © 2004 Wiley Periodicals, Inc.

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