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

Symmetry Integrability and Geometry-Methods and Applications

article

Jérôme Dubois¹  Igor G. Korepanov²  Evgeniy V. Martyushev² 

[1] Institut de Mathématiques de Jussieu, Université Paris Diderot-Paris 7;South Ural State University

关键词: Pachner moves;    Reidemeister torsion;    framed knots;    dif ferential relations in Euclidean geometry;    topological quantum field theory;   

DOI  :  10.3842/SIGMA.2010.032

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown