Lectures on open book decompositions and contact structures

Abstract

These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is to sketch a proof of Giroux correspondence between open book decompositions of three manifolds and contact structures, and then discuss various applications of this correspondence.

38 pages, 19 figures, many typos corrected and an error in Lemma 3.5 corrected

References in corpus (3)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On the classification of tight contact structures I
• Overtwisted open books from sobering arcs

Cited by in corpus (48)

• Bimodules in bordered Heegaard Floer homology
• Ozsvath-Szabo invariants and tight contact three-manifolds, I
• Khovanov homology detects the trefoils
• Planar open books, monodromy factorizations, and symplectic fillings
• Real map germs and higher open books
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds
• A class of non-fillable contact structures
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Braided embeddings of contact 3-manifolds in the standard contact 5-sphere
• Operations on open book foliations
• First steps in stable Hamiltonian topology
• Comultiplicativity of the Ozsvath-Szabo contact invariant
• Dehn Twists in Heegaard Floer Homology
• Planar open books with four binding components
• Quasipositive links and Stein surfaces
• Transverse Surgery on Knots in Contact 3-Manifolds
• On the support genus of a contact structure
• Lectures on Contact Geometry in Low-Dimensional Topology
• Planar Contact Structures with Binding Number Three
• Gabor frames from contact geometry in models of the primary visual cortex
• On the relative Giroux correspondence
• Classification of tight contact structures on surgeries on the figure-eight knot
• Computing the Thurston-Bennequin invariant in open books
• Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact Invariants
• Filling braided links with trisected surfaces
• Augmentations and ruling polynomials for Legendrian graphs
• An open book decomposition compatible with rational contact surgery
• On loose Legendrian knots in rational homology spheres
• Strong fillability and the Weinstein conjecture
• Nested open books and the binding sum
• La courbe en huit sur les sphères à pointes et le noeud de huit
• Local geometry of symplectic divisors with applications to contact torus bundles
• Holomorphic discs and surgery exact triangles
• On naturality of the Ozsvath-Szabo contact invariant
• On overtwisted, right-veering open books
• Torsion and Open Book Decompositions
• An Ozsvath-Szabo Floer homology invariant of knots in a contact manifold
• The genus zero, 3-component fibered links in $S^3$
• Minimal contact triangulations of 3-manifolds
• Fibered knots and links in lens spaces
• Admissible transverse surgery does not preserve tightness
• Computing rotation numbers in open books
• Open books supporting overtwisted contact structures and Stallings twist
• Giroux correspondence, confoliations, and symplectic structures on S^1 x M
• Twist left-veering open books, overtwistedness, looseness and virtual looseness
• On open books and embedding of smooth and contact manifolds
• On open books for nonorientable 3-manifolds