 
Summary: Proceedings of 8th
G¨okova
GeometryTopology Conference,
pp, 1 12
Variations on FintushelStern Knot Surgery on
4manifolds
Selman Akbulut
Abstract. We discuss some consequences FintushelStern `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 4manifold 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
