Reduction of framed links to the ordinary one
by
V. Kurlin
Moscow State University

We shall consider only unordered nonorientable 1-dimensional links in 3-sphere. We assign for each m-component framed link the 2m-component ordinary link such that two framed links are isotopic if and only if the corresponding ordinary links are isotopic. Also we prove we following analogue of classical Markov theorem for framed braids : two framed braids have isotopic closures if and only if one can be obtained from the other by a finite sequence of analogues of Markov transformations. As an application we obtain a representation method of 3-manifolds by framed braids and analogue of Kirby calculus on framed braids : two framed braids represent homeomorphic 3-manifolods if and only if one can be obtained from the other by a finite sequence of analogues of Markov and Kirby transformations.

Date received: June 11, 1999