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Quantum SU(2)-invariants dominate Casson's SU(2)-invariant

Published online by Cambridge University Press:  24 October 2008

Hitoshi Murakami
Hitoshi Murakami
Affiliation:
Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, 558, Japan
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Extract

In 1988, E. Witten proposed an array of invariants (quantum G-invariants) for a 3-manifold associated with a compact simple Lie group G based on the quantum field theory [22]. N. Reshetikhin and V. Turaev [20] gave a mathematical approach to these invariants for G = SU(2) by using representations of the quantum group Uq(sl(2, ℂ)). See also [2, 11, 12, 14, 15, 16] for other approaches to these invariants: [16] may be the simplest way (for knot theorists) to understand the existence of these invariants.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 2 , March 1994 , pp. 253 - 281
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

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