Invariants of knots, surfaces in \(\mathbb R^3\), and foliations. (Ukrainian, English) Zbl 1150.57003
Ukr. Mat. Zh. 59, No. 9, 1239-1252 (2007); translation in Ukr. Math. J. 59, No. 9, 1385-1396 (2007).
Summary: We give a survey of some known results related to combinatorial and geometric properties of finite-order invariants of knots in a three-dimensional space. We study the relationship between Vassiliev invariants and some classical numerical invariants of J. S. Birman and W. W. Menasco [Topology 33, No. 3, 525–556 (1994); erratum ibid. 37, No. 1, 225 (1998; Zbl 0833.57004)] and other authors. We study the reductions of link diagrams in the context of finding the braid index of links.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
