Volume 8, issue 3 (2008)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Twisted link theory

Mario O Bourgoin

Algebraic & Geometric Topology 8 (2008) 1249–1279
Abstract

We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation I–bundles over closed but not necessarily orientable surfaces. We call these twisted virtual links and show that they subsume the virtual knots introduced by L Kauffman and the projective links introduced by Yu V Drobotukhina. We show that these links have unique minimal genus three-manifolds. We use link diagrams to define an extension of the Jones polynomial for these links and show that this polynomial fails to distinguish two-colorable links over nonorientable surfaces from non-two-colorable virtual links.

Keywords
virtual link, projective link, stable equivalence, Jones polynomial, fundamental group
Mathematical Subject Classification 2000
Primary: 57M25, 57M27, 57M15, 57M05
References
Publication
Received: 10 August 2006
Accepted: 14 November 2007
Published: 26 July 2008
Authors
Mario O Bourgoin
Department of Mathematics
Brandeis University
415 South Street, MS 050
Waltham, MA 02454
USA
http://people.brandeis.edu/~mob/