Volume 15, issue 3 (2015)

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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Essential surfaces in highly twisted link complements

Ryan Blair, David Futer and Maggy Tomova

Algebraic & Geometric Topology 15 (2015) 1501–1523
Abstract

We prove that in the complement of a highly twisted link, all closed, essential, meridionally incompressible surfaces must have high genus. The genus bound is proportional to the number of crossings per twist region. A similar result holds for surfaces with meridional boundary: such a surface either has large negative Euler characteristic or is an n–punctured sphere visible in the diagram.

Keywords
essential surface, augmented link, hyperbolic link, highly twisted link, twist region, genus bound
Mathematical Subject Classification 2010
Primary: 57M25, 57M50
References
Publication
Received: 12 February 2014
Revised: 4 August 2014
Accepted: 11 September 2014
Published: 19 June 2015
Authors
Ryan Blair
Department of Mathematics and Statistics
California State University, Long Beach
1250 Bellflower Blvd
Long Beach, CA 90840
USA
http://www.csulb.edu/~rblair/
David Futer
Department of Mathematics
Temple University
1805 North Broad St.
Philadelphia, PA 19122
USA
http://www.math.temple.edu/~dfuter/
Maggy Tomova
Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City, IA 52242-1419
USA
http://www.math.uiowa.edu/~mtomova/