Modul:   MAT789  Quantum Topology Seminar

Equivalence relations on 3-manifolds defined by the lower central series of the Torelli group

Vortrag von Prof. Dr. Gwénaël Massuyeau

Sprecher eingeladen von: Prof. Dr. Anna Beliakova

Datum: 17.03.11  Zeit: 10.15 - 12.00  Raum: Y27H26

Let k be a positive integer. Two 3-manifolds M and M' are said to be "Y_k-equivalent" if M' can be obtained from M by "twisting" an embedded surface E of M with an element of the k-th term of the lower central series of the Torelli group of E. In this talk, we shall review some of the general properties of the Y_k-equivalence relation and its connections with the Goussarov-Habiro theory of finite-type invariants. Next, we will restrict to homology cylinders and we shall see how the Y_3-equivalence relation is characterized by three classical invariants. This is joint work with J.-B. Meilhan.