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2008 Twisted link theory
Mario O Bourgoin
Algebr. Geom. Topol. 8(3): 1249-1279 (2008). 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.

Citation

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Mario O Bourgoin. "Twisted link theory." Algebr. Geom. Topol. 8 (3) 1249 - 1279, 2008. https://doi.org/10.2140/agt.2008.8.1249

Information

Received: 10 August 2006; Accepted: 14 November 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1149.57004
MathSciNet: MR2443243
Digital Object Identifier: 10.2140/agt.2008.8.1249

Subjects:
Primary: 57M05, 57M15, 57M25, 57M27

Rights: Copyright © 2008 Mathematical Sciences Publishers

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Vol.8 • No. 3 • 2008
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