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We study the monopole h-invariants of 3-manifolds from a topologicalperspective based on Lidman and Manolescu's description of monopole Floerhomology in terms of Seiberg-Witten-Floer homotopy types. We investigate thepossible dependence on the choice of coefficients and give proofs of severalproperties of the h-invariants which are well known to experts, but hard totrack down in the literature.

The monopole h-invariants from a topological perspective