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KNOT SURGERY AND SCHARLEMANN MANIFOLDS SELMAN AKBULUT
 

Summary: KNOT SURGERY AND SCHARLEMANN MANIFOLDS
SELMAN AKBULUT
Abstract. We discuss the relation between Fintushel-Stern knot
surgery operation on 4-manifolds and "Scharlemann manifolds",
and as a corollary show that they all are standard. Along the way
we show the fishtail can exotically knot in S4
infinitely many ways.
0. Introduction
Let X be a smooth 4-manifold, and T2
D2
X be an imbedded
torus with trivial normal bundle, and K S3
be a knot, N(K) be its
tubular neighborhood. The Fintushel-Stern knot surgery operation is
the operation of replacing T2
D2
with (S3
- N(K)) S1
, so that the
meridian p D2

  

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

 

Collections: Mathematics