We compute the -equivariant monopole Floer homology for the class of plumbed 3-manifolds considered by Ozsváth and Szabó . We show that for these manifolds, the -equivariant monopole Floer homology can be calculated in terms of the Heegaard Floer/monopole Floer lattice complex defined by Némethi . Moreover, we prove that in such cases the ranks of the usual monopole Floer homology groups suffice to determine both the Manolescu correction terms and the -homology as an Abelian group. As an application, we show that for all plumbed 3-manifolds with at most one “bad” vertex, proving (an analogue of) a conjecture posed by Manolescu . Our proof also generalizes results by Stipsicz  and Ue  relating with the Ozsváth–Szabó -invariant. Some observations aimed at extending our computations to manifolds with more than one bad vertex are included at the end of the paper.
"On the -Equivariant Monopole Floer Homology of Plumbed 3-Manifolds." Michigan Math. J. 67 (2) 423 - 447, May 2018. https://doi.org/10.1307/mmj/1523498585