Book Review: Introduction to various aspects of degree theory in Banach spaces
Klaus Deimling · Bulletin of the American Mathematical Society · 1987
REVIEWSHowever, as up-to-date as this volume is, the field is moving so quickly that a student will not find enough about the topics of interest in today's research.Representation theory dominates today, with spectacular achievements in the representation theory of the groups of Lie type and whole new areas starting up in general representation theory.The use now of representation theory as a tool for studying structure of simple groups is very minimal, though in the long run one suspects this will not remain the case.The other very active area of finite group theory is the study of more geometrical approaches.These ideas, in particular, the amalgam method introduced by Goldschmidt, have blossomed and have applications to structural questions.Indeed, some of the proofs of the basic "pushing up" theorems in local methods, which Suzuki exposits so well, are fast becoming obsolete due to these much more powerful geometric methods.The quickness of progress in finite group theory will no doubt continue to plague authors of books on the subject.