Speaker
Prof.
Yuta Nozaki
(Yokohama)
Description
A homology cylinder is a 3-manifold that is homologically the product of a surface and an interval.
In this talk, we introduce the Reidemeister-Turaev torsion of homology cylinders which takes values in the K_1-group of the I-adic completion of the group ring of the fundamental group of a surface over the rationals, and prove that its reduction by the ideal \hat{I}^{d+1} is a finite-type invariant of degree d.
We also show that the 1-loop part of the LMO homomorphism and the Enomoto-Satoh trace can be recovered from the leading term of our torsion.
This is joint work with Masatoshi Sato and Masaaki Suzuki.
