A slicing obstruction from the 10/8 theorem

TL;DR

This paper introduces a new smooth slicing obstruction for knots derived from Furuta's 10/8 theorem, capable of detecting torsion elements and distinguishing topologically slice knots that are not smoothly slice.

Contribution

It develops a novel slicing obstruction based on the 10/8 theorem, expanding tools for studying knot concordance and smooth versus topological sliceness.

Findings

Detects torsion elements in the smooth concordance group

Identifies topologically slice knots that are not smoothly slice

Extends the application of the 10/8 theorem to knot theory

Abstract

From Furuta's $\frac{10}{8}$ theorem, we derive a smooth slicing obstruction for knots in $S^3$ using a spin $4$-manifold whose boundary is $0$-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly slice.