# Seminar by Jean-Baptiste Meilhan

Title: Torelli group and equivalence relations for homology cylinders

2013.10.21 | Christine Dilling

 Date Wed 05 Oct Time 16:15 — 17:15 Location Aud D.3

Abstract:

Two 3-manifolds are called Y_k-equivalent if one can be obtained from the other by "twisting" an embedded surface by an element of the k-th term of the lower central series of its Torelli group. The J_k-equivalence relation is defined similarly, using the Johnson filtration instead of the lower central series. In this talk, we shall consider these equivalence relation among homology cylinders over a given surface S, which are 3-manifolds homologically equivalent to S \times [0,1]. We classify these equivalence relations, for k \le 3, using several classical invariants. This provides generalizations of results of W.Pitsch and S.Morita on the structure of integral homology spheres and the Casson invariant.
This is a joint work with G. Massuyeau.

Seminar