Algebraic & Geometric Topology

A geometric interpretation of Milnor's triple linking numbers

Blake Mellor and Paul Melvin

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Abstract

Milnor’s triple linking numbers of a link in the 3–sphere are interpreted geometrically in terms of the pattern of intersections of the Seifert surfaces of the components of the link. This generalizes the well known formula as an algebraic count of triple points when the pairwise linking numbers vanish.

Article information

Source
Algebr. Geom. Topol., Volume 3, Number 1 (2003), 557-568.

Dates
Received: 7 June 2003
Accepted: 16 June 2003
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882383

Digital Object Identifier
doi:10.2140/agt.2003.3.557

Mathematical Reviews number (MathSciNet)
MR1997329

Zentralblatt MATH identifier
1040.57007

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Keywords
$\bar\mu$–invariants Seifert surfaces link homotopy

Citation

Mellor, Blake; Melvin, Paul. A geometric interpretation of Milnor's triple linking numbers. Algebr. Geom. Topol. 3 (2003), no. 1, 557--568. doi:10.2140/agt.2003.3.557. https://projecteuclid.org/euclid.agt/1513882383


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References

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