Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 1 (2015), 231-286.
Nongeneric $J$–holomorphic curves and singular inflation
This paper investigates the geometry of a symplectic –manifold relative to a –holomorphic normal crossing divisor . Extending work by Biran, we give conditions under which a homology class with nontrivial Gromov invariant has an embedded –holomorphic representative for some –compatible . This holds for example if the class can be represented by an embedded sphere, or if the components of are spheres with self-intersection . We also show that inflation relative to is always possible, a result that allows one to calculate the relative symplectic cone. It also has important applications to various embedding problems, for example of ellipsoids or Lagrangian submanifolds.
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 231-286.
Received: 3 December 2013
Revised: 16 June 2014
Accepted: 18 June 2014
First available in Project Euclid: 16 November 2017
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McDuff, Dusa; Opshtein, Emmanuel. Nongeneric $J$–holomorphic curves and singular inflation. Algebr. Geom. Topol. 15 (2015), no. 1, 231--286. doi:10.2140/agt.2015.15.231. https://projecteuclid.org/euclid.agt/1510840912