scholarly journals Kirby calculus for null-homologous framed links in 3-manifolds

2017 ◽  
Vol 10 (2) ◽  
pp. 585-631
Author(s):  
Kazuo Habiro ◽  
Tamara Widmer
Keyword(s):  
Kirby Calculus

Kirby calculus

1999 ◽  
pp. 139-196 ◽  
Author(s):  
Robert Gompf ◽  
András Stipsicz
Keyword(s):  
Kirby Calculus

scholarly journals Refined Kirby calculus for integral homology spheres

2006 ◽  
Vol 10 (3) ◽  
pp. 1285-1317 ◽  
Author(s):  
Kazuo Habiro
Keyword(s):  
Integral Homology ◽  
Kirby Calculus

scholarly journals On Kirby calculus for null-homotopic framed links in 3–manifolds

2014 ◽  
Vol 14 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Kazuo Habiro ◽  
Tamara Widmer
Keyword(s):  
Kirby Calculus

scholarly journals Special Heegaard diagrams and the Kirby calculus

1990 ◽  
Vol 37 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Eduardo Rêgo ◽  
Eugénia César de Sá
Keyword(s):  
Heegaard Diagrams ◽  
Kirby Calculus

4-Manifolds and Kirby Calculus

1999 ◽  
Author(s):  
Robert Gompf ◽  
András Stipsicz
Keyword(s):  
Kirby Calculus

scholarly journals VIRTUAL KNOT DIAGRAMS AND THE WITTEN–RESHETIKHIN–TURAEV INVARIANT

2005 ◽  
Vol 14 (08) ◽  
pp. 1045-1075 ◽  
Author(s):  
H. A. DYE ◽  
LOUIS H. KAUFFMAN
Keyword(s):  
Fundamental Group ◽  
Virtual Link ◽  
Virtual Knot ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Classical Link ◽  
Kirby Calculus ◽  
Knot Diagrams

The Witten–Reshetikhin–Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kirby calculus. As a result, it is also an invariant of the 3-manifolds represented by the classical link diagrams. This generalization is used to demonstrate that there are virtual knot diagrams with a non-trivial Witten–Reshetikhin–Turaev invariant and trivial 3-manifold fundamental group.

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