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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A geometric interpretation of Milnor's triple linking numbers

Blake Mellor and Paul Melvin

Algebraic & Geometric Topology 3 (2003) 557–568

arXiv: math.GT/0110001

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.

Keywords
$\bar\mu$–invariants, Seifert surfaces, link homotopy
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
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Publication
Received: 7 June 2003
Accepted: 16 June 2003
Published: 19 June 2003
Authors
Blake Mellor
Loyola Marymount University
One LMU Drive
Los Angeles, CA 90045
USA
Paul Melvin
Bryn Mawr College
101 N merion Ave
Bryn Mawr PA 19010-2899
USA