Kazuo Habiro : Refined Kirby calculus for closed 3-manifolds

Abstract:
A celebrated theorem of Kirby states that two framed links in the 3-sphere
yield orientation-preserving diffeomorphic 3-manifolds by surgery
if and only if they are related by a finite sequence of two kinds of moves:
stabilizations and handle slides.  I gave a version of this result
for framed links whose linking matrix is diagonal with diagonal entries \pm1,
which works as "refined Kirby calculus" for integral homology spheres.
Later, Fujiwara generalized this result to rational homology spheres
of a certain type. In this talk, I will discuss a generalization of
these results for closed 3-manifolds with no restriction on homology groups.