Indefinite Stein fillings and Pin(2)-monopole Floer homology

TL;DR

This paper establishes obstructions to certain intersection forms of Stein fillings of specific rational homology spheres using Pin(2)-monopole Floer homology, advancing understanding of 4-manifold topology.

Contribution

It introduces new obstructions based on Pin(2)-monopole Floer homology for Stein fillings of rational homology spheres with specific properties.

Findings

Obstructions to non-negative definite intersection forms.

Application of Pin(2)-monopole Floer homology techniques.

Generalizations to broader classes of 3-manifolds.

Abstract

Given a spin$^c$ rational homology sphere $(Y,\mathfrak{s})$ with $\mathfrak{s}$ self-conjugate and for which the reduced monopole Floer homology $\mathit{HM}_{\bullet}(Y,\mathfrak{s})$ has rank one, we provide obstructions to the intersection forms of its Stein fillings which are not negative definite. The proof of this result (and of its natural generalizations we discuss) uses $\mathrm{Pin}(2)$-monopole Floer homology.