Invariants of contact structures from open books
By John B. Etnyre, Burak Ozbagci. 2006
88 citations recorded by the source corpus.
In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact structure), the binding number (which is the minimal number of binding components of a supporting open book for the contact structure with minimal genus pages) and the norm (which is minus the maximal Euler characteristic of a page of a supporting open book).
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/be103f28ed7466c0ce3bf79c8bfec966a9b54e2b
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Heegaard Floer homology and genus one, one‐boundary component open books (2008, background): “(In fact, whenever ν is a diffeomorphism of a genus g surface S with one boundary component, which commutes with the hyperelliptic involution (as depicted in Figure 2) on S, the Spin structure associated to the contact structure ξS,ν is self-conjugate (see [8]).”
- Essential open book foliations and fractional Dehn twist coefficient (2012, unknown): “,γjφ ′ ∗(γ −1 j ) + where a1,...,ag′,b1,...,bg′,C1,...,Ck,c1,...,cn are the standard generators of π1(S′). The term γjφ′∗ (γ−1 j ) is represented by a closed curve because φ ′ = idnear C1,...,Ck. See [15] for a more detailed proof. This presentation shows that the curves c1,...,cn are not null-homot”