Institut für Mathematik


Konferenz: Kazuo Habiro: Special talks

Refined Kirby calculus for closed 3-manifolds

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.