Lectures on Holomorphic Curves in Symplectic and Contact Geometry

Abstract

This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here. Further chapters will be added in future updates.

194 pages; v2 has some corrections and additions to what was in v1 - no new chapters, but there are substantial new sections covering the contractibility of the space of tame almost complex structures, positivity of intersections, and marked point constraints (including a proof that curves of small index are generically immersed)

References in corpus (3)

• Relative asymptotic behavior of pseudoholomorphic half-cylinders
• Polyfolds And A General Fredholm Theory
• Giroux torsion and twisted coefficients

Cited by in corpus (14)

• Contact homology and virtual fundamental cycles
• On partially wrapped Fukaya categories
• Automatic transversality in contact homology II: filtrations and computations
• $S^1$-invariant symplectic hypersurfaces in dimension $6$ and the Fano condition
• Contact 3-manifolds, holomorphic curves and intersection theory
• Emergent Spacetime and Cosmic Inflation
• On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
• Morse theory methods for a class of quasi-linear elliptic systems of higher order
• Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems
• Automatic transversality in contact homology I: Regularity
• Intersection of almost complex submanifolds
• Essential tori in spaces of symplectic embeddings
• A four-dimensional mapping class group relation
• Towards Homological Mirror Symmetry