Surgical distance between lens spaces

TL;DR

This paper investigates the minimal number of Dehn surgeries needed to transform one lens space into another, contributing to the understanding of the surgical distance between 3-manifolds.

Contribution

It introduces the concept of surgical distance between lens spaces and analyzes the minimal length of surgery sequences connecting them.

Findings

Established bounds for the surgical distance between lens spaces.

Identified cases where the minimal sequence length is achieved.

Provided new insights into the complexity of 3-manifold transformations.

Abstract

It is well-known that any pair of closed orientable 3-manifolds are related by a finite sequence of Dehn surgeries on knots. Furthermore Kawauchi showed that such knots can be taken to be hyperbolic. In this article, we consider the minimal length of such sequences connecting a pair of 3-manifolds, in particular, a pair of lens spaces.