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On genericity for holomorphic curves in four-dimensional almost-complex manifolds |
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| Authors: | Helmut Hofer Véronique Lizan Jean-Claude Sikorav |
| Affiliation: | 1. Courant Institute, New-York University, 251 Mercer Street, 10012, New-York, NY, USA 2. U.F.R. Sciences, Mathématiques, I.U.F.M. de Toulouse, 118, route de Narbonne, F-31078, Toulouse cedex 4 3. Laboratoire Emile Picard, UMR CNRS 5578, Université Paul Sabatier, 118, route de Narbonne, F-31062, Toulouse |
| Abstract: | We consider spaces of immersed (pseudo-)holomorphic curves in an almost complex manifold of dimension four. We assume that they are either closed or compact with boundary in a fixed totally real surface, so that the equation for these curves is elliptic and has a Fredholm index. We prove that this equation is regular if the Chern class is ≥ 1 (in the case with boundary, if the ambient Maslov number is ≥ 1). Then the spaces of holomorphic curves considered will be manifolds of dimension equal to the index. |
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