

Geometric Topology Seminar
August 3, 2017 14:00–17:00, Moscow, Steklov Mathematical Institute, room 534






A combinatorial formula for Minvariant
P. M. Akhmet'ev^{} 
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Abstract:
Minvariant of isotopy classes for classical 3component links are welldefined using an integral formula over a finitedimensional configuration space of the links. Therefore this invariant is a finitetype invariant
(of the order 7 in the sense of Vassiliev). This invariant is used for physical applications to investigate properties of magnetostatic configuration in the ideal magnetohydrodynamics.
This invariant is a polynomial function of the first two coefficients of the normalized Conway polynomial for proper sublinks:(C_0(1,2) С_0(2,3), C_0(3,1), C_1(1), C_1(2), C_1(3), C_1(1,2), C_1(2,3), C_1(3,1), C_1(1,2,3); the collection of 10 variables). An explicit expression is known up to an odd polynomial of the order not great then 7 of pairwise linking numbers of the components С_0(1,2), C_0(2,3), C_0(3,1).
Nevertheless, one may calculate Minvariant for an arbitrary 3component links using the following additional normalization property (this is a new result): For the standard Hopf 3component links the value of M equals to +1.
Language: English

