Trivial-torsion conjecture for four-longitude sutured monopole Floer homology

Let $G_{\mathrm{tor}}$ be the torsion group appearing in Lemma 4. The group is associated to the monopole Floer homology computation for the closure of $(V,\gamma^4)\sqcup(V,\gamma^4)$.

Trivial-torsion conjecture. The torsion group $G_{\mathrm{tor}}$ in Lemma 4 is trivial:

$$G_{\mathrm{tor}}=0.$$

The conjecture arises from an expected direct computation of the monopole Floer homology of a particular closure constructed by Kronheimer and Mrowka. The preceding rank calculations constrain the torsion, but do not determine it completely.