Finite order corks

TL;DR

This paper constructs finite order Stein corks with boundaries as cyclic branched covers of slice knots, providing a method to generate numerous finite order corks, including some that are not Stein corks.

Contribution

It introduces a general method to produce finite order Stein corks and extends to examples of finite order corks that may not be Stein corks.

Findings

Existence of order n Stein corks for any positive integer n

Boundaries are cyclic branched covers of slice knots

Method to produce many finite order corks, including non-Stein corks

Abstract

We show that for any po sitive integer $m$, there exist order $n$ Stein corks. The boundaries are cyclic branched covers of slice knots embedded in the boundary of corks. By applying these corks to generalized forms, we give a method producing examples of many finite order corks, which are possibly not Stein cork.