Finite type invariants of knots and 3-manifolds (Q2917451)

This is a short survey of the theory of finite-type invariants for knots and 3-manifolds. Section 2 surveys the Vassiliev invariants (finite-type invariants), the Kontsevich invariant (universal finite-type invariant) of knots, and relations among these invariants and quantum invariants.NEWLINENEWLINESection three gives a survey on finite-type invariants of integral homology 3-spheres and the Le-Murakami-Ohtsuki (LMO) invariant of 3-manifolds and relations among these invariants and perturbative invariants.NEWLINENEWLINESection 4 considers related topics such as Habiro's reconstruction of finite-type invariants by using a series of equivalence relations among 3-manifolds, Goussarov et al.'s extension of the set of knots by Gauss diagrams, and finally Vassiliev invariants as mapping degrees of configuration spaces.