Work

A relation between Milnor’s μ-invariants and HOMFLYPT polynomials

Year: 2016

Type: article

Abstract: Polyak showed that any Milnor’s [Formula: see text]-invariant of length 3 can be represented as a combination of the Conway polynomials of knots obtained by certain band sum of the link components. On the other hand, Habegger and Lin showed that Milnor invariants are also invariants for string links, called [Formula: see text]-invariants. We show that any Milnor’s [Formula: see text]-invariant of length [Formula: see text] can be represented as a combination of the HOMFLYPT polynomials of knots obtained from the string link by some operation, if all [Formula: see text]-invariants of length [Formula: see text] vanish. Moreover, [Formula: see text]-invariants of length [Formula: see text] are given by a combination of the Conway polynomials and linking numbers without any vanishing assumption.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216516500723

Author: Yuka Kotorii

Institution: The University of Tokyo

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Award: Finite type invariants and Milnor invariants by clasper theory