Simplicial complexes offer a window into the structure of many topological spaces, both through the study of simplicial homology and also by allowing mathematicians to visualize many topological spaces as homeomorphic to various simplical complexes. In addition, group actions on simplicial complexes are very tractable, and so by studying how a group acts on a simplicial complex, a topologist can learn about how the group acts on an underlying topological space. This is an introductory talk, and can be appreciated by anyone with familiarity with basic topology or group theory. We begin by reviewing simplicial complexes, then investigate the quotient spaces induced by a group action. We conclude with a useful theorem about the regularity of certain simplicial complexes, and a few examples. Depending on the time used, Mathew Titus may begin talking on the next section in the text we are going through:
Based on: pages 226-234., Katsuo Kawakubo: The theory of transformation groups.