An RBG construction of integral surgery homeomorphisms

TL;DR

This paper extends the RBG construction to generate knot pairs with identical n-surgeries and explores their potential in constructing exotic definite four-manifolds via n-surgery homeomorphisms.

Contribution

It generalizes the RBG construction for knots and investigates applications to exotic four-manifolds.

Findings

Constructed new examples of knots with the same n-surgery

Analyzed the implications for exotic four-manifold construction

Provided a framework for future topological explorations

Abstract

We generalize the RBG construction of Manolescu and Piccirillo to produce pairs of knots with the same $n$-surgery, and investigate the possibility of constructing exotic definite four-manifolds using $n$-surgery homeomorphisms.