Cohomology rings, Rochlin function, linking pairing and the Goussarov-Habiro theory of three-manifolds.
Reidemeister-Turaev torsion modulo one of rational homology threespheres.
Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant
Let be a compact connected oriented surface with one boundary component, and let be the fundamental group of . The Johnson filtration is a decreasing sequence of subgroups of the Torelli group of , whose -th term consists of the self-homeomorphisms of that act trivially at the level of the -th nilpotent quotient of . Morita defined a homomorphism from the -th term of the Johnson filtration to the third homology group of the -th nilpotent quotient of . In this paper, we replace groups...
An introduction to the abelian Reidemeister torsion of three-dimensional manifolds
These notes accompany some lectures given at the autumn school “” in October 2009. The abelian Reidemeister torsion for -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.
Fox pairings and generalized Dehn twists
We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi–Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.
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