Contents
1 Introduction
2 Homology cobordisms and homology cylinders
2.1 Definition of the monoids
2.2 The mapping class group and the Torelli group
2.3 The closure construction
2.4 The closed case and the bordered case
3 Johnson homomorphisms and Morita homomorphisms
3.1 The Dehn–Nielsen representation
4 The LMO homomorphism
4.1 The algebra of symplectic Jacobi diagrams
5 The $\delta Y$-filtration on the monoid of homology cylinders
5.1 The $Y_{k}$-equivalence relation
6 The Lie ring of homology cylinders
6.1 Definition of the Lie ring of homology cylinders
7 The homology cobordism group
7.1 Definition of the homology cobordism group