Infinite Group Actions on Polyhedra

Michael Davis received a PhD in mathematics from Princeton University in 1975. He was Professor of Mathematics at Ohio State University for thirty nine years, retiring in 2022 as Professor Emeritus. In 2015 he became a Fellow of the AMS. His research is in geometric group theory and topology. Since 1981 his work has focused on topics related to reflection groups including the construction of new examples of aspherical manifolds and the study of their properties.

• Part I: Introduction.- 1 Introduction.- Part II: Nonpositively curved cube complexes.- 2 Polyhedral preliminaries.- 3 Right-angled spaces and groups.- Part III: Coxeter groups, Artin groups, buildings.- 4 Coxeter groups, Artin groups, buildings.- Part IV: More on NPC cube complexes.- 5 General theory of cube complexes.- 6 Hyperbolization.- 7 Morse theory and Bestvina–Brady groups.- Appendix A: Complexes of groups.

“The author made the right choice not to include proofs of the theorems stated (otherwise the size of the book would have increased by almost an order of magnitude) but only to indicate the sources where such proofs can be found. This implies a certain degree of maturity and knowledge in the reader. For this reason, the text is dedicated to advanced graduate students or to researchers.” (Egle Bettio, zbMATH 1542.20002, 2024)