Preface and Acknowledgments As will be indicated in a moment in the Introduction, this book is primarily intended as an exposition—which hopes to bring a wider audience into contact with an area of research that I have enjoyed working in, over many years. But of course during those years, I gained much of my own experience by benefiting from the knowledge of very many colleagues. So in this preface, I would first like to take the opportunity to thank them—apologizing in advance to anyone I may have left out. (Of course the reader will see the work of these experts emerging, as the later exposition in the book proceeds.) Some personal acknowledgments. My introduction to the methods of fi- nite geometry dates mainly to my collaboration with Mark Ronan, beginning around 1979. I also learned a great deal about geometries from Bill Kantor, Jon Hall, Don Higman, Ernie Shult, Francis Buekenhout, and Bruce Cooperstein. During the 1980s, many experts in finite group theory, motivated partly by the work of Tits on buildings, became interested in geometries underlying simple groups. I particularly benefited from long-term contact with Michael Aschbacher, Franz Timmesfeld, and Geoff Robinson. Discussions with Peter Webb and Jacques Th´ evenaz were instrumental in lead- ing me into the more specifically topological methods underlying subgroup com- plexes and in effect led to my later collaboration with Dave Benson. Many other topologists helped educate me in their area particular Alejandro Adem, Jim Mil- gram, Bill Dwyer, Bob Oliver, and Jesper Grodal. Especially in recent years it has been a pleasure to discuss developments made by John Maginnis and Silvia Onofrei. Also during the 1970s and 1980s, many combinatorialists (notably Stanley) were also developing similar techniques for the combinatorics of posets (partially ordered sets). Some of my initial contacts with that area were around 1981 with Jim Walker and Bob Proctor. Soon thereafter I began a particularly valuable ongoing correspondence with Anders Bj¨ orner. Over the years I have also profited from discussions with other experts—notably Volkmar Welker, Michelle Wachs, and John Shareshian. And of course we also learn from our students: It was a pleasure to work with Peter Johnson, Andrew Mathas, Matt Bardoe, Kristin Umland, and Phil Grizzard—who wrote their theses with me at the University of Illinois at Chicago (UIC), in aspects of this general research area. I also had some involvement in the thesis work of Tony Fisher under George Glauberman, and of Paul Hewitt under Jon Hall. xi
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