Algebraic & Geometric Topology

A geometric interpretation of Milnor's triple linking numbers

Blake Mellor and Paul Melvin

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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