Twisted link theory

Bourgoin, Mario O¹

¹Department of Mathematics, Brandeis University, 415 South Street, MS 050, Waltham, MA 02454, USA

Algebraic and Geometric Topology, Tome 8 (2008) no. 3, pp. 1249-1279

Résumé

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.

Détail

DOI : 10.2140/agt.2008.8.1249

Keywords: virtual link, projective link, stable equivalence, Jones polynomial, fundamental group

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