## 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)

### Keywords:

knot invariants; configuration spaces

Zbl 0863.57004