Right-veering diffeomorphisms of compact surfaces with boundary

By K. Honda, W. Kazez, G. Matić. 2005

206 citations recorded by the source corpus.

We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight contact structures and open book decompositions.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6a54886b9b34d65c1d2b44184c14b60fba0b7881

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Cabling, contact structures and mapping class monoids (2010, background): “[27]) that Strong(Σ) ⊂ HFH (Σ) and the other two inclusions follow from [36] as it is well known that a weakly fillable contact structure or one with non-vanishing Heegaard Floer invariant is tight.”
The contact invariant in sutured Floer homology (2007, background): “Consider a partial open book decomposition (S, h) for (M, , ξ). The notion of a rightveering (S, h) can be defined in the same way as in [ HKM1 ]: If for every x ∈ ∂P − and every properly embedded arc a ⊂ P which begins at x and has both endpoints on ∂P − , h(a) is to the right of a, then we say (S,”
Sutures and contact homology I (2010, methodology): “10 is analogous to a theorem of Honda, Kazez and Matić [22] for sutured Floer homology.”
Planar open books, monodromy factorizations and symplectic fillings (2009, unknown): “One related condition is the right-veering property of an open book [14]; indeed, a contact structure is tight if and only if every compatible open book is right-veering.”