Orateur:
Timur Nasybullov (Universita di Bologna)
Titre: Complete invariant for fused links and homology of finite
covers via quantum representations.
Résumé:
One of the most important problems in knot theory is the knot recognition
problem, is determining the equivalence of two knots. A complete algorithmic
solution of 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.