The character degree simplicial complex of a finite group

The character degree graph Γ(G)Γ(G) of a finite group G has long been studied as a means of understanding the structural properties of G  . For example, a result of Manz and Pálfy states that the character degree graph of a finite solvable group has at most two connected components. In this paper, we introduce the character degree simplicial complex G(G)G(G) of a finite group G  . We provide examples justifying the study of this simplicial complex as opposed to Γ(G)Γ(G), and prove an analogue of Manz's Theorem on the number of connected components that is dependent upon the dimension of G(G)G(G).