Connected components of generalized strata of meromorphic differentials with residue conditions

Generalized strata of meromorphic differentials are loci within the usual strata of differentials where certain sets of residues sum to zero. They naturally appear in the boundary of the multi-scale compactification of the usual strata. The classification of generalized strata is a key step towards understanding the irreducible components of the boundary strata of the multi-scale compactification. The connected components of generalized strata of residueless differentials were classified in \cite{lee2023connected}. In the present paper, we classify the connected components of generalized strata of meromorphic differentials in full generality.