Lectures on open book decompositions and contact structures

By John B. Etnyre. 2004

245 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d26a8d805d2b5a426f04e77b25b83b778f659c38

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Heegaard Floer homology and genus one, one‐boundary component open books (2008, background): “Many details are omitted here, but can be found in [37] and [6].”
Ozsvth-Szab invariants and tight contact 3-manifolds, III (2007, background): “From now on, we refer to [7] for standard facts on contact structures and their compatible open books.”
Cabling, contact structures and mapping class monoids (2010, background): “7 is a small modification of Thurston and Winkelnkemper’s original proof for honest open books [51], cf [17].”
Planar open books and Floer homology (2005, unknown): “S G ] 20 A pr”
Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “Acknowledgements We are grateful to John Etnyre for some helpful conversations, to Dan Margalit and Chris Wendl for helpful correspondence, and to Paolo Lisca and András Stipsicz for their comments on a preliminary version of this paper.”
On the equivalence of Legendrian and transverse invariants in knot Floer homology (2011, background): “We would like to thank Vincent Colin, John Etnyre and Lenny Ng for helpful conversations.”
Heegard Floer invariants of Legendrian knots in contact three-manifolds (2008, methodology): “Definition 2.1 (Giroux) A contact structure ξ and an open book decomposition are compatible if ξ , as a cooriented 2–plane field, is the kernel of a contact one–form α with the property that dα is a symplectic form on each page, hence orients both the page and the binding, and with this orientation ”
NOTIONS OF POSITIVITY AND THE OZSVÁTH–SZABÓ CONCORDANCE INVARIANT (2005, background): “NOTIONS OF POSITIVITY AND THE OZSVÁTH-SZABÓ CONCORDANCE INVARIANT 3 Noting that σi,j is of the form wσj−1w −1 with w ∈ Bn, the weaker notion of a quasipositive knot is any knot which can be realized as the closure of a braid of the form: β = Πmk=1wkσikw −1 k .”