I will describe some results concerning factorizations of diffeomorphisms of compact surfaces with boundary into positive Dehn twists. In particular, I will describe a refinement of the right-veering property, and discuss some applications to the characterization of geometric properties of contact structures on three-manifolds in terms of monodromies of supporting open book decompositions.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/249