On right-veering diffeomorphisms and binding sums

Orbegozo Rodriguez, Miguel (2023) On right-veering diffeomorphisms and binding sums. PhD thesis, University of Glasgow.

Abstract

This thesis consists of two parts, more or less independent of each other but both devoted to the study of open book decompositions of 3-manifolds and their relationship to contact structures.

Right-veering diffeomorphisms are related to tightness of contact structures due to a result of Honda, Kazez, and Matić but it is in general difficult to determine whether a given diffeomorphism is right-veering. In the first part we prove that the right-veering property can be detected in a combinatorial way.

In the second part, we explore properties of an operation of contact manifolds (with a prescribed open book) called the binding sum. We show that even if the summands are Stein fillable the result of the sum need not be, and indeed can be overtwisted. We also provide an explicit computation of vanishing of the Heegaard Floer contact class for an infinite family of such sums where the summands are Stein fillable.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Supervisor's Name: Wand, Dr. Andy
• Date of Award: 2023
• Depositing User: Theses Team
• Unique ID: glathesis:2023-84008
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 21 Dec 2023 09:15
• Last Modified: 21 Dec 2023 13:43
• Thesis DOI: 10.5525/gla.thesis.84008
• URI: https://theses.gla.ac.uk/id/eprint/84008