Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008



J. Korean Math. Soc. 2024; 61(1): 1-28

Online first article December 20, 2023      Printed January 1, 2024

Copyright © The Korean Mathematical Society.

Periodic surface homeomorphisms and contact structures

Dheeraj Kulkarni, Kashyap Rajeevsarathy, Kuldeep Saha

Bhopal Bypass Road, Bhauri; Bhopal Bypass Road, Bhauri; Sector V, Salt Lake, Kolkata 700091


In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.

Keywords: Periodic map, rational open book, contact structure

MSC numbers: Primary 57K33, 57D20; Secondary 57M50

Supported by: The work in this article is supported by the grant EMR/2017/000727 by SERB, Government of India.