Refined Kirby calculus for integral homology spheres
Abstract
A theorem of Kirby states that two framed links in the 3-sphere produce orientation-preserving homeomorphic results of surgery if they are related by a sequence of stabilization and handle-slide moves. The purpose of the present paper is twofold: First, we give a sufficient condition for a sequence of handle-slides on framed links to be able to be replaced with a sequences of algebraically canceling pairs of handle-slides. Then, using the first result, we obtain a refinement of Kirby's calculus for integral homology spheres which involves only +/-1-framed links with zero linking numbers.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- September 2005
- DOI:
- arXiv:
- arXiv:math/0509039
- Bibcode:
- 2005math......9039H
- Keywords:
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- Mathematics - Geometric Topology;
- Mathematics - Quantum Algebra;
- 57M25;
- 57M27
- E-Print:
- This is the version published by Geometry &