Vortrag von Prof. Dr. Kazuo Habiro Datum: 12.04.10 Zeit: 14.00 - 16.00 Raum: Y27H46

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 for rational homology spheres whose homology and linking pairing
are the same as lens spaces of type (p,1), where p is an odd prime. In this
talk, I will discuss a generalization of these results for closed 3-manifolds
with no restriction on homology groups, realized by surgery along framed links
whose linking matrix is a block sum of a fixed nondegenerate symmetric integer
matrix, a zero matrix of a fixed size, and a diagonal matrix with diagonal
entries \pm1.