Special moves for open book decompositions of 3-manifolds-Reference-Cited by-同舟云学术

Special moves for open book decompositions of 3-manifolds

Published:2018-10 Issue:11 Volume:27 Page:1843008
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Piergallini Riccardo¹,Zuddas Daniele²

Affiliation:

1. Università di Camerino, Scuola di Scienze e Tecnologie, via Madonna delle Carceri 9, Camerino 62032, Italy

2. Lehrstuhl Mathematik VIII, Mathematisches Institut der Universität Bayreuth, NW II, Universitätsstr. 30, 95447 Bayreuth, Germany

Abstract

We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer’s twisting, which is presented in two different (but stably equivalent) forms. Our approach relies on 4-dimensional Lefschetz fibrations, and on 3-dimensional contact topology, via the Giroux-Goodman stable equivalence theorem for open book decompositions representing homologous contact structures.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216518430083

Reference17 articles.

1. A Lemma on Systems of Knotted Curves

2. Lefschetz fibrations over the disc

3. Lutz Twist and Contact Surgery

4. Constructing symplectic forms on 4–manifolds which vanish on circles

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