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Proceedings of 8th Geometry-Topology Conference,

Summary: Proceedings of 8th
Geometry-Topology Conference,
pp, 1 ­ 12
Variations on Fintushel-Stern Knot Surgery on
Selman Akbulut
Abstract. We discuss some consequences Fintushel-Stern `knot surgery' operation
coming from its handlebody description. We give some generalizations of this opera-
tion and give a counterexample to their conjecture.
1. Introduction
Let X be a smooth 4-manifold and K S3
be a knot, In [4] among other things
Fintushel and Stern had shown that the operation K XK of replacing a tubular
neighborhood of imbedded torus in X by (S3
- K) × S1
could results change of smooth
structure of X. In [1] an algorithm of describing handlebody of XK in terms of the
handlebody of X was described. In this article we will give some corollaries of this
construction, and present a counterexample to conjecture of Fintushel and Stern which


Source: Akbulut, Selman - Department of Mathematics, Michigan State University


Collections: Mathematics