Problems of growth and rationality in algebra and topology

Abstract

CONTENTS Introduction Chapter I. Problems of growth and rationality § 1. Growth functions, growth, Poincaré and Hilbert series § 2. Problems of growth and rationality § 3. A discussion of the problems of growth and rationality Chapter II. Interconnections between the problems of rationality § 1. The graded algebra associated with a nilpotent algebra § 2. Some definitions and constructions § 3. Four-dimensional CW-complexes and local rings § 4. Relations between Poincaré series of local rings and loop spaces Chapter III. Poincaré series and growth § 1. Generating functions, algebraic and topological properties of objects, and growth § 2. Poincaré series of k-connected spaces Chapter IV. A discussion of examples of non-rationality and intermediate growth § 1. Graded and nilpotent algebras § 2. Local rings and CW-complexes § 3. Some remarks and questions References