Automatic transversality and orbifolds of punctured holomorphic curves in dimension four

By Chris Wendl. 2008

160 citations recorded by the source corpus.

We derive a numerical criterion for J-holomorphic curves in 4-dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results of Hofer-Lizan-Sikorav [HLS97] and Ivashkovich-Shevchishin [IS99] to allow punctured curves with boundary that generally need not be somewhere injective or immersed. As an application, we combine this with the intersection theory of punctured holomorphic curves to prove that certain geometrically natural moduli spaces are globally smooth orbifolds, consisting generically of embedded curves, plus unbranched multiple covers that form isolated orbifold singularities.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6b9f78b4b4debf2a5ba354ee9c99d323fd4a329d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Torsion contact forms in three dimensions have two or infinitely many Reeb orbits (2017, background): “1], and see [29] for more general automatic transversality results.”
Lagrangian spheres, symplectic surfaces and the symplectic mapping class group (2010, background): “s, [u] is the relative homology class of u([15]). The following is a very special case of a theorem due to Wendl, which states that for certain u, the SFT regularity is automatic. Theorem 2.1 (Wendl, [59]). Suppose (W,J) is a 4-dimensional almost complex manifold with cylindrical end modelled on con”
Cylindrical contact homology for dynamically convex contact forms in three dimensions (2014, unknown): “Much more general automatic transversality results are proved in [27], but we recall the proof of this simple lemma for the convenience of the reader.”
Lecture Notes on Embedded Contact Homology (2013, background): “This and much more general automatic transversality results are proved in [62].”