North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the localization and completion of topological spaces, model categories, and Hopf algebras. The first half of the book sets out the basic theory of localization and completion of nilpotent spaces, using the most elementary treatment the authors know of. It makes no use of simplicial techniques or model categories, and it provides full details of other necessary preliminaries. With these topics as motivation, most of the second half of the book sets out the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and homological algebra are treated in parallel. A short last part develops the basic theory of bialgebras and Hopf algebras.

Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.

This volume contains articles written by the invited speakers and workshop participants from the conference on "Crystallographic Groups and Their Generalizations", held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.

This volume presents a cross-section of new developments in algebraic topology. The main portion consists of survey articles suitable for advanced graduate students and professionals pursuing research in this area. A great variety of topics are covered, many of which are of interest to researchers working in other areas of mathematics. In addition, some of the articles cover topics in group theory and homological algebra.

This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.