Twisted link theory

By Mario O. Bourgoin. 2006

51 citations recorded by the source corpus.

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. 57M25, 57M27, 57M15, 57M05

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ff4b49b8f1ebb0c9103b18e033c95a3f2323fdf4

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Parity in knot theory (2010, background): “There are many generalisations of the Kauffman bracket to virtual knots; see, for example, papers [8], [25]–[27] and the references there.”