Compatible relative open books on relative contact pairs via generalized square bridge diagrams

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ARIKAN M. F., TAŞPINAR İ. Ö.

Acta Mathematica Hungarica, vol.172, no.1, pp.80-118, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 172 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1007/s10474-024-01402-5
  • Journal Name: Acta Mathematica Hungarica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet
  • Page Numbers: pp.80-118
  • Keywords: 57R65, 58A05, 58D27, contact structure, Legendrian, monodromy, open book, square bridge, surgery
  • Middle East Technical University Affiliated: Yes

Abstract

Using square bridge position, Akbulut-Ozbagci and later Arikan gave algorithms both of which construct an explicit compatible open book decomposition on a closed contact 3-manifold which results from a contact (±1)-surgery on a Legendrian link in the standard contact 3-sphere. In this article, we introduce the “generalized square bridge position” for a Legendrian link in the standard contact 5-sphere and partially generalize this result to the dimension five via an algorithm which constructs relative open book decompositions on relative contact pairs.