Asian Journal of Mathematics

Volume 21 (2017)

Number 2

A combinatorial algorithm for computing higher order linking numbers

Pages: 265 – 286



Chun-Chung Hsieh (Institute of Mathematics, Academia Sinica, Taipei, Taiwan)

Louis Kauffman (Department of Mathematics, University of Illinois, Chicago, Il., U.S.A.)

Chichen M. Tsau (Department of Mathematics and Computer Science, Saint Louis University, St. Louis, Missouri, U.S.A.)


We develop the intersection theory at relative chain-cochain level, and apply it along with the use of Seifert disks for an oriented link to give a combinatorial algorithm to compute Massey’s higher order linking numbers and therefore Milnor numbers.


linking number, higher order linking number, cohomology operation, knots, links, Seifert disks, intersection product, cup product, Massey product

2010 Mathematics Subject Classification


Received 8 August 2014

Published 5 July 2017