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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 032, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.032 (Mi sigma489) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds

Jérôme Duboisa, Igor G. Korepanovb, Evgeniy V. Martyushevb

a Institut de Mathématiques de Jussieu, Université Paris Diderot-Paris 7, UFR de Mathématiques, Case 7012, Bâtiment Chevaleret, 2, place Jussieu, 75205 Paris Cedex 13, France
b South Ural State University, 76 Lenin Avenue, Chelyabinsk 454080, Russia
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DOI: https://doi.org/10.3842/SIGMA.2010.032
Abstract: We present an invariant of a three-dimensional manifold with a framed knot in it based on the Reidemeister torsion of an acyclic complex of Euclidean geometric origin. To show its nontriviality, we calculate the invariant for some framed (un)knots in lens spaces. Our invariant is related to a finite-dimensional fermionic topological quantum field theory.
Keywords: Pachner moves; Reidemeister torsion; framed knots; differential relations in Euclidean geometry; topological quantum field theory.
Received: October 9, 2009; in final form April 7, 2010; Published online April 15, 2010
Bibliographic databases:
Document Type: Article
MSC: 57M27; 57Q10; 57R56
Language: English
Citation: Jérôme Dubois, Igor G. Korepanov, Evgeniy V. Martyushev, “A Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds”, SIGMA, 6 (2010), 032, 29 pp.
Citation in format AMSBIB
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\by J\'er\^ome Dubois, Igor G.~Korepanov, Evgeniy V.~Martyushev
\paper A~Euclidean Geometric Invariant of Framed (Un)Knots in Manifolds
\jour SIGMA
\yr 2010
\vol 6
\papernumber 032
\totalpages 29
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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