On the intersection forms of spin four-manifolds with boundary

TL;DR

This paper establishes new bounds on the intersection forms of spin four-manifolds with boundary, using a novel invariant derived from equivariant Seiberg-Witten Floer K-theory, potentially impacting the 11/8 conjecture.

Contribution

It introduces a new numerical invariant for homology spheres and the concept of Floer K_G-split homology spheres, advancing the study of intersection forms in spin cobordisms.

Findings

Proves Furuta-type bounds for intersection forms.

Defines a new invariant from Pin(2)-equivariant Seiberg-Witten Floer K-theory.

Introduces the notion of Floer K_G-split homology spheres.

Abstract

We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory. In the process we introduce the notion of a Floer K_G-split homology sphere; this concept may be useful in an approach to the 11/8 conjecture.