Abstract
We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation –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.
Citation
Mario O Bourgoin. "Twisted link theory." Algebr. Geom. Topol. 8 (3) 1249 - 1279, 2008. https://doi.org/10.2140/agt.2008.8.1249
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