  We study the monopole h-invariants of 3-manifolds from a topological
perspective based on Lidman and Manolescu's description of monopole Floer
homology in terms of Seiberg-Witten-Floer homotopy types. We investigate the
possible dependence on the choice of coefficients and give proofs of several
properties of the h-invariants which are well known to experts, but hard to
track down in the literature.
