WikiProject Mathematics (Rated B-class, Mid-importance)
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Mathematics rating:
 B Class
 Mid Importance
Field: Topology

## Major Revision

I have revised the article thoroughly, adding several pictures and incorporating material from the old linking coefficient article. The material on self-linking number has been moved to a separate article. Jim 03:05, 26 July 2007 (UTC) This article doesn't seem to include the linking of two simple closed curves in 3-manifolds other than the 3-sphere. In general, such linking numbers will be fractions, or simply undefined, depending on the homology of the curves. I'm not sure of the source of this learning, having received it by word of mouth from Ralph Fox. -- Ken Perko 69.113.192.109 (talk) 04:00, 24 July 2015 (UTC) (lbrtpl@gmail.com)

Kissing number? How the hell is that supposed to be related? —Preceding unsigned comment added by 141.84.69.20 (talk) 22:27, 11 December 2009 (UTC)

## Since when are cup products a generalization of linking numbers???

One sentence under Generalizations reads as follows:

"In algebraic topology, the cup product is a far-reaching algebraic generalization of the linking number, with the Massey products being the algebraic analogs for the Milnor invariants."

To the best of my knowledge, cup products (of cohomology classes) in manifolds are not directly relevant to any linking numbers. Rather, they are dual to the intersection pairing on homology.

(It is true that the intersection of homology classes can be used in the definition of linking number. But the intersection of homology classes is definitely not the same as linking number per se.

So, this sentence needs to be radically altered.Daqu (talk) 04:32, 30 January 2013 (UTC)