Volume 20, issue 4 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The dihedral genus of a knot

Patricia Cahn and Alexandra Kjuchukova

Algebraic & Geometric Topology 20 (2020) 1939–1963

Let K S3 be a Fox p–colored knot and assume K bounds a locally flat surface S B4 over which the given p–coloring extends. This coloring of S induces a dihedral branched cover X S4. Its branching set is a closed surface embedded in S4 locally flatly away from one singularity whose link is K. When S is homotopy ribbon and X a definite four-manifold, a condition relating the signature of X and the Murasugi signature of K guarantees that S in fact realizes the four-genus of K. We exhibit an infinite family of knots Km with this property, each with a Fox 3–colored surface of minimal genus m. As a consequence, we classify the signatures of manifolds X which arise as dihedral covers of S4 in the above sense.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

knot, branched cover, ribbon genus, trisection
Mathematical Subject Classification 2010
Primary: 57M12, 57M25, 57Q60
Received: 29 December 2018
Revised: 24 July 2019
Accepted: 25 October 2019
Published: 20 July 2020
Patricia Cahn
Department of Mathematics and Statistics
Smith College
Northampton, MA
United States
Alexandra Kjuchukova
Max Planck Institute for Mathematics