Introductory Lectures on Contact Geometry

By John B. Etnyre. 2001

144 citations recorded by the source corpus.

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a0e5984b75c7ac327c7d5e143a2c02d7fc8438a2

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Non-Abelian localization for Chern-Simons theory (2005, background): “We first review a few basic facts about such manifolds, for which a complete reference is [36] For simplicity, we begin by assuming that the three-manifold M admits a free U (1) action.”
Lectures on open book decompositions and contact structures (2004, background): “Having read [15] should be sufficient background for this paper.”
Contact 3-manifolds with infinitely many Stein fillings (2003, background): “(For the relevant definitions see [6], [11].”
NOTIONS OF POSITIVITY AND THE OZSVÁTH–SZABÓ CONCORDANCE INVARIANT (2005, background): “Rudolph showed in [34] thatD+(K, n) is strongly quasipositive if and only if n ≤ TB(K), where TB(K) denotes the maximal Thurston-Bennequin number of K [9].”
Fibered Transverse Knots and the Bennequin Bound (2008, background): “Moreover, suppose L is a fibered link in a 3-manifold M and the fibration (L, π,Σ) supports a tight contact structure with Giroux torsion equal to zero.”
Cobordisms of sutured manifolds and the functoriality of link Floer homology (2009, result): “think of γas a thickened oriented 1-manifold. We now review some fundamental notions and results about contact structures and set our orientation conventions; for more details see the notes of Etnyre [6] and the bookofGeiges[9]. Let Mbe anoriented3-manifold. A contact structure ξon M is a nowhere in”
Legendrian and Transversal Knots (2003, background): “opology at the level of [70]. We have tried to keep the contact geometry prerequisites to a minimum, but it would certainly be helpful to have had some prior exposure to the basics as can be found in [31, 46]. Some of the proofs in Section 5 rely on convex surface theory which can be found in [31], ”
Four dimensions from two in symplectic topology (2002, background): “nt(γ) belongs to an open half-space, then γ([0,τ]) = γ([0,1]) deﬁnes a sphere – and hence is not a candidate for an overtwisted disk. Exercise 9.12. Check that the characteristic foliation (deﬁned in [11]) on the overtwisted disk Din the preceding proof is exactly the degenerate characteristic folia”
Surgery diagrams for contact 3-manifolds (2003, methodology): “For the contact-geometric part of the proof we use the language of convex surfaces and dividing curves; for a brief introduction see [7].”
Rational linking and contact geometry (2009, methodology): “We can use the exponential map to identify a neighborhood of the zero section of i∗ξ|∂Σ with an r–fold cover of a tubular neighborhood of K.”