Configuration spaces and imbedding problems. (English) Zbl 0874.57006

Andersen, Jørgen Ellegaard (ed.) et al., Geometry and physics. Proceedings of the conference at Aarhus University, Aarhus, Denmark, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 184, 135-140 (1997).
The author’s introduction: “The purpose of this talk is to present joint work with Clifford Taubes on a purely topological approach towards the recent physics-inspired self-linking invariants for knots described by Dror Bar-Natan and Guadagnini, Martinelli, and Mintchev. As I hope to show, the configuration spaces and their natural compactifications à la Fulton and MacPherson are precisely the needed ingredients to explain these invariants and their generalizations.”
Starting from the Gauss integral formula for the linking number of two circles in \(\mathbb{R}^3\), the author sketches a development leading to knot invariants which are also related to work of Kontsevich. The main underlying theme is the standard volume form \(\omega\) on \(S^2\) and integrating various products of pullbacks of \(\omega\) over appropriate compactifications of configuration spaces.
For the entire collection see [Zbl 0855.00020].


57M25 Knots and links in the \(3\)-sphere (MSC2010)