Volume 16, issue 6 (2016)

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

Volume 22, 1 issue

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
Essential twisted surfaces in alternating link complements

Marc Lackenby and Jessica S Purcell

Algebraic & Geometric Topology 16 (2016) 3209–3270

Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement.

alternating links, essential surfaces
Mathematical Subject Classification 2010
Primary: 57M25
Received: 11 December 2014
Revised: 23 March 2016
Accepted: 21 April 2016
Published: 15 December 2016
Marc Lackenby
Mathematical Institute
University of Oxford
Radcliffe Observatory Quarter
Woodstock Road
United Kingdom
Jessica S Purcell
School of Mathematical Sciences
Monash University
9 Rainforest Walk
Room 401
Monash University VIC 3800