Contact 3-manifolds, holomorphic curves and intersection theory
Abstract
This is a revision of some expository lecture notes written originally for a 5-hour minicourse on the intersection theory of punctured holomorphic curves and its applications in 3-dimensional contact topology. The main lectures are aimed primarily at students and require only a minimal background in holomorphic curve theory, as the emphasis is on topological rather than analytical issues. Some of the gaps in the analysis are then filled in by the appendices, which include self-contained proofs of the similarity principle and positivity of intersections, and conclude with a "quick reference" for the benefit of researchers, detailing the basic facts of Siefring's intersection theory.
Cite
@article{arxiv.1706.05540,
title = {Contact 3-manifolds, holomorphic curves and intersection theory},
author = {Chris Wendl},
journal= {arXiv preprint arXiv:1706.05540},
year = {2019}
}
Comments
170 pages, 20 figures; v2 is an extensive revision, with a new introduction and expanded appendices (including a self-contained proof of positivity of intersections, new material on intersection products of holomorphic buildings, and a comparison of conventions with the ECH literature). To appear as a book in the Cambridge Tracts in Mathematics series with Cambridge University Press