Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PERIODIC SURFACE HOMEOMORPHISMS AND CONTACT STRUCTURES

  • Dheeraj Kulkarni (Department of Mathematics Indian Institute of Science Education and Research Bhopal) ;
  • Kashyap Rajeevsarathy (Department of Mathematics Indian Institute of Science Education and Research Bhopal) ;
  • Kuldeep Saha (Institute for Advancing Intelligence (IAI) TCG-CREST)
  • Received : 2022.05.19
  • Accepted : 2023.09.22
  • Published : 2024.01.01
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Abstract

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.

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Acknowledgement

The work in this article is supported by the grant EMR/2017/000727 by SERB, Government of India. The first author would also like to thank James Conway for noting an error in the earlier draft of the article and for helpful conversations. The authors thank the referees for numerous suggestions to improve exposition and clarity.

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