I am (still) reading Evasiveness of Graph Properties and Topological Fixed Point Theorems. On page 52 it states:
Suppose that $H$ is a group of order $p^m$. With $m \geq 1$, which acts on $\Delta$ in such a way that $\Delta^h$ is a subcomplex for any $h \in H$. Then $\Delta^H$ is $\mathbb{F}_p$ acylic.
I am assume that $h : \Delta \to \Delta$ where $\Delta$ is a simplicial complex. Thus $\Delta^h$ I believe is just the image of $h$ on $\Delta$. But what is $\Delta^H$? Stating that $\Delta^H$ is acyclic leads me to believe it is a simplicial complex. However, as every $h \in H$ is also a simplicial complex I am lead to believe $\Delta^H$ is a collection of simplicial complexes. What is $\Delta^H$?