Geodesic
A geometric interpretation of Milnor’s triple linking numbers
Mellor, Blake1 ; Melvin, Paul2
1Loyola Marymount University, One LMU Drive, Los Angeles, CA 90045, USA
2Bryn Mawr College, 101 N merion Ave, Bryn Mawr PA 19010-2899, USA
Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 557-568
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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.

DOI : 10.2140/agt.2003.3.557
Keywords: $\bar\mu$–invariants, Seifert surfaces, link homotopy

Mellor, Blake  1   ; Melvin, Paul  2

1 Loyola Marymount University, One LMU Drive, Los Angeles, CA 90045, USA
2 Bryn Mawr College, 101 N merion Ave, Bryn Mawr PA 19010-2899, USA 
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Mellor, Blake; Melvin, Paul. A geometric interpretation of Milnor’s triple linking numbers. Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 557-568. doi: 10.2140/agt.2003.3.557

[1] T D Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Mem. Amer. Math. Soc. 84 (1990)

[2] R A Fenn, Techniques of geometric topology, London Mathematical Society Lecture Note Series 57, Cambridge University Press (1983)

[3] W Magnus, A Karrass, D Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers, New York–London–Sydney (1966)

[4] J Milnor, Isotopy of links. Algebraic geometry and topology, from: "A symposium in honor of S. Lefschetz", Princeton University Press (1957) 280

[5] V G Turaev, The Milnor invariants and Massey products, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 66 (1976) 189, 209

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