On the construction of knots and links from Thompson’s groups. (English) Zbl 1423.57013

Jones, Vaughan F. R.

Adams, Colin C. (ed.) et al., Knots, low-dimensional topology and applications. Knots in Hellas, International Olympic Academy, Greece, July 2016. Papers of the international conference, Ancient Olympia, Greece, July 17–23, 2016. Cham: Springer. Springer Proc. Math. Stat. 284, 43-66 (2019).

Summary: We review recent developments in the theory of Thompson group representations related to knot theory.
For the entire collection see [Zbl 1419.57001].

MSC:

57M25	Knots and links in the \(3\)-sphere (MSC2010)
57-02	Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57M27	Invariants of knots and \(3\)-manifolds (MSC2010)
20F36	Braid groups; Artin groups
20F38	Other groups related to topology or analysis
22D10	Unitary representations of locally compact groups

Keywords:

Thompson group; knot; link; braid; representation; skein theory