×

Configuration spaces and imbedding invariants. (English) Zbl 0880.57002

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.

MSC:

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

Citations:

Zbl 0863.57004
PDF BibTeX XML Cite