Linking in knot theory
by
Chun-Chung Hsieh
Math. Dept., Academia Sinica, Taiwan
Coauthors: Chun-Chung Hsieh, L.H. Kauffman

Invented by W. Massey, J. Milnor and E. Witten, linking theory is a numerical invariant of knot theory, but the explicit formulae is still missing.

In this talk, I will present the joint work with L.H. Kauffman on the first non-vanishing linkings from both Massey-Milnor and Chern-Simons-Witten aspects, aiming at the combinatorial formulae thereof.

Part I. I will define the Massey-Milnor linking and compute the combinatorial formulae explicitly.

Part II. I will talk about perturbative Chern-Simons-Witten theory and express the related linking theory explicitly in terms of Feynman diagrams.

Part III. I will show that Massey-Milnor linking is exactly the same as Chern-Simons-Witten theory.

Date received: January 8, 2005