(Université de Bologne)
Knot theory is a branch of low-dimensional topology which was firstly developed by A.-T. Vandermonde in the end of 18th century. Deep mathematical studies of knots was initiated by K.-F. Gauss in the 19th century, and during 150 years there were formulated and solved a lot of problems of knot theory which have a vast number of applications abroad the mathematics.
One of the most important problems in knot theory is a knot recognition problem, is determining the equivalence of two knots. A complete algorithmic solution to this problem exists but it has unknown complexity.
Virtual knot theory is a generalization of classical knot theory which was introduced by L.Kauffman in 1999. For virtual knots it is also very important to solve the knot recognition problem.
In the talk I am going to introduce one simplification of classical and virtual knot theories called fused knot theory and solve the knot recognition problem for fused links in polynomial time.