Configuration spaces and imbedding invariants. (English) Zbl 0880.57002

Bott, Raoul

Turk. J. Math. 20, No. 1, 1-17 (1996).

The author gives, first, an expository account of his work, jointly with C. Taubes, published in the article [J. Math. Phys. 35, No. 10, 5247-5287 (1994; Zbl 0863.57004)]. There they initiated the use of the configuration spaces of \(S^1\) and \(\mathbb{R}^3\), respectively, in the study of knots of \(S^1\) in \(\mathbb{R}^3\). Subsequently, they noted that these methods apply equally well to the study of higher dimensional knots of \(S^{2k-1}\) in \(\mathbb{R}^{2k+1}\). A sketch of this extension is given in the last section of this article.

Reviewer: S.Y.Husseini (Madison)

MSC:

57M25

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

Keywords:

knot invariants; configuration spaces

Citations:

Zbl 0863.57004