Book chapter
Braids, Fibered Knots, and Concordance Questions
Research Directions in Symplectic and Contact Geometry and Topology, pp.293-324
Association for Women in Mathematics Series, Springer International Publishing
08/09/2022
DOI: 10.1007/978-3-030-80979-9_7
Abstract
Given a knot in S3, one can associate to it a surface diffeomorphism in two different ways. First, an arbitrary knot in S3 can be represented by braids, which can be thought of as diffeomorphisms of punctured disks. Second, if the knot is fibered—that is, if its complement fibers over S1—one can consider the monodromy of the fibration. One can ask to what extent properties of these surface diffeomorphisms dictate topological properties of the corresponding knot. In this article we collect observations, conjectures, and questions addressing this, from both the braid perspective and the fibered knot perspective. We particularly focus on exploring whether properties of the surface diffeomorphisms relate to four-dimensional topological properties of knots such as the slice genus.
Details
- Title: Subtitle
- Braids, Fibered Knots, and Concordance Questions
- Creators
- Diana Hubbard - Brooklyn CollegeKeiko Kawamuro - University of IowaFeride Ceren Kose - The University of Texas at AustinGage Martin - Boston CollegeOlga Plamenevskaya - Stony Brook UniversityKatherine Raoux - Michigan State UniversityLinh Truong - Institute for Advanced StudyHannah Turner - The University of Texas at Austin
- Resource Type
- Book chapter
- Publication Details
- Research Directions in Symplectic and Contact Geometry and Topology, pp.293-324
- Series
- Association for Women in Mathematics Series
- DOI
- 10.1007/978-3-030-80979-9_7
- eISSN
- 2364-5741
- ISSN
- 2364-5733
- Publisher
- Springer International Publishing; Cham
- Language
- English
- Date published
- 08/09/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984240775402771
Metrics
28 Record Views