# Higher cup products on hypercubic lattices: application to lattice models of topological phases

@inproceedings{Chen2021HigherCP, title={Higher cup products on hypercubic lattices: application to lattice models of topological phases}, author={Yu-An Chen and Sri Ramya Tata}, year={2021} }

In this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation on the simplicial complexes. We illustrate how this formalism can elucidate lattice constructions on hypercubic lattices for various models and deriving them from spacetime actions. In particular, we demonstrate explicitly that the (3+1)D SPT S = 12 ∫ w 22 + w 41 (where w 1 and w 2 are the ﬁrst and second Stiefel-Whitney classes) is dual to the…

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