Genus of The Hypercube Graph And Real Moment-Angle Complexes

Abstract

In this paper we demonstrate a calculation to find the genus of the hypercube graph $Q_n$ using real moment-angle complex $\mathcal{Z}_\mathcal{K}(D^1,S^0)$ where $\mathcal{K}$ is the boundary of an $n$-gon. We also calculate an upper bound for the genus of the quotient graph $Q_n/C_n$, where $C_n$ represents the cyclic group with $n$ elements.