Periodic Surface Homeomorphisms and Contact Structures

Dheeraj Kulkarni, Kashyap Rajeevsarathy, Kuldeep Saha

Published 2020-07-29Version 1

We study the contact structures coming from a natural class of rational open books, in the sense of Baker-Etnyre-Morris, that correspond to the conjugacy classes of periodic surface diffeomorphisms. By considering the contact structures associated to such rational open books, we prove some fillability results for such contact structures. We also prove an analogue of Mori's construction of explicit symplectic filling for rational open books. We also prove a sufficient condition for Stein fillability of rational open books analogous to the positivity of monodromy in honest open books as in the result of Giroux and Loi-Piergallini.