Geometry and Topology

Proof of the Shubert theorem

A. M. Kulakova

Chelyabinsk State University

Abstract: The famous Schubert theorem states that every nontrivial knot on S3 admits a unique decomposition into connecetd sum of priem knots. The proof was very cumbersome and took more than 40 pages. In this papper we describe another short proof of the Schubert theorem, which is based on the theory of the roots of topological objects, discovered by S. Matveev.

Keywords: knot, connected sum, prime decomposition.