Annulus twist and diffeomorphic 4-manifolds II

TL;DR

This paper proves that for any integer framing, there are infinitely many distinct knots that produce the same 4-manifold when used in 2-handle additions, advancing understanding of 4-manifold topology.

Contribution

It solves a strong version of Kirby's Problem 3.6(D), demonstrating the existence of infinitely many knots with identical 4-manifold outcomes for any framing.

Findings

Existence of infinitely many mutually distinct knots for any framing n

Different knots can produce the same 4-manifold via 2-handle addition

Advances understanding of knot surgery and 4-manifold invariants

Abstract

We solve a strong version of Problem 3.6 (D) in Kirby's list, that is, we show that for any integer $n$, there exist infinitely many mutually distinct knots such that $2$-handle additions along them with framing $n$ yield the same $4$-manifold.