Floer homology for 2-torsion instanton invariants

TL;DR

This paper develops a new Floer homology variant for 2-torsion instanton invariants, proving a gluing formula and demonstrating non-triviality of Donaldson invariants for certain 4-manifolds, along with non-existence results.

Contribution

It introduces a novel Floer homology variant for 2-torsion instanton invariants, with a gluing formula and applications to Donaldson invariants and 4-manifold topology.

Findings

Proved a gluing formula for the new Floer homology variant.

Showed non-triviality of Donaldson invariants for connected sums of 4-manifolds.

Established non-existence of certain compact, spin 4-manifolds with boundary.

Abstract

We construct a variant of Floer homology groups and prove a gluing formula for a variant of Donaldson invariants. As a corollary, the variant of Donaldson invariants is non-trivial for connected sums of 4-manifolds which satisfy a condition for Donaldson invariants. We also show a non-existence result of compact, spin 4-manifolds with boundary some homology 3-spheres and with certain intersection forms.