Plachta L. Knot invariants and surfaces in 3-dimensional space

The properties of knot and link invariants of finite order in 3-dimensional space are investigated. The connection between Vassiliev knot invariants and sattelite operations is founded. Some new corelations between Vassiliev knot invariants and classical geometric knot invariants are obtained. The reduction operations on link diagrams in the context of calculating the braid index of links and the Jones conjecture are investigated. The combinatorial and geo-metric description of tiled incompressible tori of standard position in closed braid complement is given. A complete topological invariant of gradient-like foliations on closed orientable surfaces is constructed.