[Z4], 05/30/22: Extensive updates described in Section 1.1
[Z1], 04/24/22: Section 6.2 added (bubbling on thin necks)
         03/26/22: Proposition 6.2 added (bubbling with marked points colliding)
         03/15/21: Section 6.1 added
         03/14/21: Section 2.2 and Examples 2.7,2.8 added
         03/10/21: statement and proof of Lemma 5.4 sharpened; Section 5.3 redone, justifying the termination in finitely many steps carefully.

• [ISh] S. Ivashkovich and V. Shevchishin, Pseudo-holomorphic curves and envelopes of meromorphy of two-spheres in CP², math.CV/9804014
  • Lemma 2.3.2 is Serre duality for real Cauchy-Riemann operators.
• [LT] J.~Li and G.~Tian, Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds, math.AG/9608032
  • Section 3 contains gluing for pseudoholomorphic maps without exponentially weighted norms on long cylinders.
• [MS98] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Mathematical Monographs, 1998/2017
  • Introduction and Chapter 1: an overiew of symplectic topology and its connections with classical mechanics; just read through this without worrying about the details.
• [MS04] D. McDuff and D. Salamon, J-Holomorphic Curves and Symplectic Topology, AMS Colloquium Publications 52, 2004/2012/2017
  • Preface and Chapter 1: a thorough overview of the book, giving a flavor of J-holomorphic curves techniques; just read through this without worrying about the details.
  • Chapter 2 establishes basic properties of J-holomorphic maps, some of which depend on the compatibility with a symplectic form and some do not.
  • Chapter 4 concerns the key rigidity and compactness type properties of J-holomorphic maps that depend heavily on the compatibility with a symplectic form (though some preliminary statements do not depend on the compactability). In a sense, this chapter establishes the foundations of the theory of pseudo-holomorphic maps; the remainder of the book is about re-packaging them for specific applications.
• [Sh] V. Shevchishin, Pseudoholomorphic curves and the symplectic isotopy problem, math/0010262
  • Lemma 2.4.1 extends the usual twisting up/down construction of complex geometry to real Cauchy-Riemann operators.
• [TZ] M. Tehrani and A. Zinger, Absolute vs. relative invariants
  • This compares the two invariants when one might hope for them to be equal.
• [Z1] A. Zinger, Notes on J-holomorphic maps
  • More systematic version of Chapters 2 and 4 of [MS04].
• [Z2] A. Zinger, Transversality for J-holomorphic maps: a complex-geometric perspective, in progress
  • More systematic analogue of Chapters 3 and 6 of [MS04].
• [Z3] A. Zinger, Basic Riemannian geometry and Sobolev estimates used in symplectic topology
  • This contains analytic estimates people in symplectic topology regularly use, but do not like bothering with their details too much.
• [Z4] A. Zinger, The determinant line bundle for Fredholm operators: construction, properties, and classification
  • This fully constructs a compatible system of determinant line bundles and describes the choices that specify such a system.
• [Z5] A. Zinger, Pseudocycles and integral homology
  • This shows that pseudocycles and integral homology classes are essentially the same thing.
• [Z6] A. Zinger, Counting plane rational curves: old and new approaches
  • Section 4 contains a proof of Kontsevich's recursion for plane rational curves, excluding the gluing part.