Bounding the Dehn surgery number by 10/8

TL;DR

This paper introduces new examples of 3-manifolds with specific properties that cannot be obtained by Dehn surgery on knots in the three-sphere, using Furuta's 10/8-theorem.

Contribution

It provides novel examples of 3-manifolds with weight one fundamental group and the same homology as lens spaces that are not knot surgeries, utilizing a simple combinatorial approach.

Findings

Identified 3-manifolds not realizable by knot surgery

Applied Furuta's 10/8-theorem in a new context

Simplified combinatorial proof technique

Abstract

We provide new examples of 3-manifolds with weight one fundamental group and the same integral homology as the lens space $L(2k,1)$ which are not surgery on any knot in the three-sphere. Our argument uses Furuta's 10/8-theorem, and is simple and combinatorial to apply.