Plakhta L. P.
Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1239–1252
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 knots and point out the role of surfaces in the investigation of these invariants. We also consider combinatorial and geometric properties of essential tori in standard position in closed braid complements by using the braid foliation technique developed by Birman, Menasco, and other authors. We study the reductions of link diagrams in the context of finding the braid index of links.
Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1431-1434
We prove that the alternating group $A_6$ cannot freely act on $(S^n)^5$ We give an example of free action of the alternating group $A_4$ on $(S^n)^3$.
Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1233-1237
Realizations of integral $D_3$-modules of rank 2 on $(S^n)^k$ for the dihedral groups $D_3$ are studied. Cohomologies of the sets of the singular points of the actions of the semidirect products $ℤ / pXℤ / q$ and the quaternion groups $Q$ on $(S^n)^k$ are investigated.