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On calculation of the Witten invariants of 3-manifolds

Part of: Topological manifolds Low-dimensional topology

Published online by Cambridge University Press:  09 April 2009

Eugene Rafikov ,
Dušan Repovš  and
Fulvia Spaggiari
Eugene Rafikov
Affiliation:
Department of Differential Geometry, Faculty of Mechanics and Mathematics Moscow State University, Moscow 119899, Russia, e-mail: rafikov@mccme.ru
Dušan Repovš
Affiliation:
Institute for Mathematics Physics and Mechanics University of Ljubljana, P.O. Box 2964, 1001 Ljubljana Slovenia, e-mail: dusan.repovs@fmf.uni-lj.si
Fulvia Spaggiari
Affiliation:
Department of Mathematics, University of Modena and Reggio EmiliaVia Campi 213/B, 41100 Modena, Italy, e-mail: spaggiari@unimo.it
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Abstract

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In this paper we present a short definition of the Witten invariants of 3-manifolds. We also give simple proofs of invariance of those obtained for r = 3 and r = 4. Our definition is extracted from the 1993 paper of Lickorish and the Prasolov-Sossinsky book, where it is dispersed over 20 pages. We show by several examples that it is indeed convenient for calculations.

Keywords

Witten invariantKauffman bracketplane diagramDehn surgery3-manifold

MSC classification

Secondary: 57M25: Knots and links in $S^3$ 57N10: Topology of general $3$-manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 3 , December 2003 , pp. 385 - 398
Copyright
Copyright © Australian Mathematical Society 2003

References

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