Twisted link theory

Bourgoin, Mario O

doi:10.2140/agt.2008.8.1249

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Twisted link theory

Mario O Bourgoin

Algebraic & Geometric Topology 8 (2008) 1249–1279

DOI: 10.2140/agt.2008.8.1249

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/

Volume 8, issue 3 (2008)