Knots and 4-manifolds

Owens, B. (2021) Knots and 4-manifolds. Winter Braids Lecture Notes, 6(2019), 2. (doi: 10.5802/wbln.28)

Abstract

These notes are based on the lectures given by the author during Winter Braids IX in Reims in March 2019. We discuss slice knots and why they are interesting, as well as some ways to decide if a given knot is or is not slice. We describe various methods for drawing diagrams of double branched covers of knots in the 3-sphere and surfaces in the 4-ball, and how these can be useful to decide if an alternating knot is slice. We include a description of the computer search for slice alternating knots due to the author and Frank Swenton.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Owens, Professor Brendan
• Authors: Owens, B.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Winter Braids Lecture Notes
• Publisher: Centre Mersenne
• ISSN: 2426-0312
• ISSN (Online): 2426-0312
• Copyright Holders: Copyright © 2021 Centre Mersenne
• First Published: First published in Winter Braids Lecture Notes 6(2019):2
• Publisher Policy: Reproduced with the permission of the publisher