Right-veering diffeomorphisms of compact surfaces with boundary II

Abstract

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group B_n on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Ro1,Ro2].

25 pages, 5 figures

References in corpus (9)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• On the classification of tight contact structures I
• Right-veering diffeomorphisms of compact surfaces with boundary II
• Compact Stein surfaces with boundary as branched covers of $\B^4$
• Symplectic fillability of tight contact structures on torus bundles
• Overtwisted open books from sobering arcs
• Tight contact structures on fibered hyperbolic 3-manifolds
• An infinite family of tight, not semi-fillable contact three-manifolds
• Pinwheels and bypasses

Cited by in corpus (53)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• Khovanov homology detects the trefoils
• Planar open books, monodromy factorizations, and symplectic fillings
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• Fractional Dehn twists in knot theory and contact topology
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Dehn surgery, rational open books and knot Floer homology
• Transverse invariants and right-veering
• Operations on open book foliations
• Tight small Seifert fibered manifolds with $e_0=-2$
• Chord diagrams, contact-topological quantum field theory, and contact categories
• A note on the knot Floer homology of fibered knots
• Planar open books with four binding components
• Contact surgery and supporting open books
• On families of fibred knots with equal Seifert forms
• Bypass attachments in higher-dimensional contact topology
• Positive factorizations of mapping classes
• Sutured Floer homology, sutured TQFT and non-commutative QFT
• Band surgeries and crossing changes between fibered links
• Khovanov homology and the cinquefoil
• Persistently foliar composite knots
• On a structure of random open books and closed braids
• On plastikstufe, bordered Legendrian open book and overtwisted contact structures
• Planar Contact Structures with Binding Number Three
• On the relative Giroux correspondence
• On a question of Etnyre and Van Horn-Morris
• Trefoil Plumbing
• Classification of tight contact structures on surgeries on the figure-eight knot
• Braids with as many full twists as strands realize the braid index
• Factorizations of diffeomorphisms of compact surfaces with boundary
• Cutting arcs for torus links and trees
• An open book decomposition compatible with rational contact surgery
• Fixed-point-free pseudo-Anosov homeomorphisms, knot Floer homology and the cinquefoil
• Khovanov homology and tight contact structures
• Stein fillable contact 3-manifolds and positive open books of genus one
• Examples of planar tight contact structures with support norm one
• The arc complex and contact geometry: non-destabilizable planar open book decompositions of the tight contact 3-sphere
• A User's Guide to Morse Foliated Open Books
• Unexpected Stein fillings, rational surface singularities, and plane curve arrangements
• Coloring Link Diagrams And Conway-type Polynomial Of Braids
• On the Classification of Planar Contact Structures
• On a relation between the self-linking number and the braid index of closed braids in open books
• Elliptic open books on torus bundles over the circle
• Fractional Dehn twists and modular invariants
• Positive factorizations of pseudoperiodic homeomorphisms
• Periodic Surface Homeomorphisms and Contact Structures
• Floer homology and right-veering monodromy
• L-spaces, taut foliations and fibered hyperbolic two-bridge links
• Kirby diagrams of 4-dimensional open books
• Floer homology, twist coefficients, and capping off
• Invariants of contact structures from open books
• Explicit horizontal open books on some Seifert fibered 3--manifolds
• On overtwisted, right-veering open books