Reidemeister torsion of 3-manifolds for SL(2 ;C)-representations
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
Reidemeister torsion is one of classical invariants for a 3-manifold with a linear representation of the fundamental group. Roughly speaking it is a function on the space of conjugacy classes of linear representations.
In 1930’s it was defined and studied by Reidemeister, Franz and de Rham to classify lens spaces. Lens space gives examples that are homotopy equivalent, but not homeomorphic.
By using Reidemeister torsion we can distinguish them up to homeomorphism.
In this talk we consider this invariant for SL(2 ;C)-irreducible representations.
In 1980’s Dennis Johnson proposed to consider a polynomial whose zero set are the set of the non-trivial values of Reidemeister torsion.
He also proved some recursive formula of this polynomial for some Brieskorn homology 3-spheres.
I shall explain some concrete examples and discuss the generalization of Johnson’s formula.
- Teruaki KITANO