Constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of $\bar{\mu}$ and $\kappa$ invariants

TL;DR

This paper establishes new constraints on the intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres, using the $ar{d}$ and $d$ invariants, and compares their relationships.

Contribution

It introduces bounds on intersection forms based on $ar{d}$ and $d$ invariants and analyzes the relationship between these invariants for Seifert rational homology 3-spheres.

Findings

The difference between $d$ and $-ar{d}$ is at most 2.

Under certain conditions, this difference is zero.

Constraints on intersection forms are derived in terms of these invariants.

Abstract

We give some constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of the $\bar{\mu}$ invariant and compare them with those in terms of the $\kappa$ invariant. We also show that the difference between $\kappa$ and $-\bar{\mu}$ for a Seifert rational homology 3-sphere is at most 2, and under certain extra conditions the difference is 0.