The Jones-Witten invariants of knots
Michael Atiyah (1989-1990)
Séminaire Bourbaki
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Displaying similar documents to “Knot theory with the Lorentz group”
The Jones-Witten invariants of knots
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Summary of the three lectures. These notes are available electronically at http://www.ma.huji.ac.il/~drorbn/Talks/Srni-9901/notes.html.
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Taizo Kanenobu (1986)
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For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements...
Virtual biquandles
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We describe new approaches for constructing virtual knot invariants. The main background of this paper comes from formulating and bringing together the ideas of biquandle [KR], [FJK], the virtual quandle [Ma2], the ideas of quaternion biquandles by Roger Fenn and Andrew Bartholomew [BF], the concepts and properties of long virtual knots [Ma10], and other ideas in the interface between classical and virtual knot theory. In the present paper we present a new algebraic construction of virtual...