Knot surgery and Scharlemann manifolds

TL;DR

This paper explores the relationship between knot surgery and Scharlemann manifolds in 4-manifolds, proving they are all standard, and demonstrates the infinite exotic knotting of fishtails in the 4-sphere.

Contribution

It establishes the equivalence of Fintushel-Stern knot surgery and Scharlemann manifolds and shows the fishtail can be exotically knotted infinitely many times in the 4-sphere.

Findings

All studied manifolds are standard.

Fishtails can be exotically knotted infinitely many ways.

The relation between knot surgery and Scharlemann manifolds is clarified.

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 that the fishtail can exotically knot in the 4-sphere infinitely many ways.