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In the literature, abelian higher gauge symmetry models are shown to be validin all finite dimensions and exhibit the characteristic behavior of SPT phasesmodels. While the ground state degeneracy and the entanglement entropy werethoroughly studied, the classification of the ground state space still remainedobscure. Based on differentio-geometric approach and, anticipating the notationof the current paper, if $\left( C_{\bullet} , \partial^C_{\bullet} \right)$ isthe chain complex associated to the geometrical content of these models, while$\left( G_{\bullet} , \partial^G_{\bullet} \right)$ is its symmetriescounterpart, we show that the ground state space is classified by a $H^0 (C,G)\times H_0 (C,G)$ group, where $H^0(C,G)$ is the $0$-th cohomology and $H_0(C,G)$ is the corresponding $0$-th homology group with coefficients in thechain complex.

A dualization approach to the Ground State Subspace Classification of Abelian Higher Gauge Symmetry Models