Connective Real $K$-Theory of Finite Groups

by Robert Ray Bruner, John Patrick Campbell Greenlees

2010 · American Mathematical Soc.

This book is about equivariant real and complex topological $K$-theory for finite groups. Its main focus is on the study of real connective $K$-theory including $ko^*(BG)$ as a ring and $ko_*(BG)$ as a module over it. In the course of their study the authors define equivariant versions of connective $KO$-theory and connective $K$-theory with reality, in the sense of Atiyah, which give well-behaved, Noetherian, uncompleted versions of the theory. They prove local cohomology and completion theorems for these theories, giving a means of calculation as well as establishing their formal credentials. In passing from the complex to the real theories in the connective case, the authors describe the known failure of descent and explain how the $\eta$-Bockstein spectral sequence provides an effective substitute. This formal framework allows the authors to give a systematic calculation scheme to quantify the expectation that $ko^*(BG)$ should be a mixture of representation theory and group cohomology. It is characteristic that this starts with $ku^*(BG)$ and then uses the local cohomology theorem and the Bockstein spectral sequence to calculate $ku_*(BG)$, $ko^*(BG)$, and $ko_*(BG)$. To give the skeleton of the answer, the authors provide a theory of $ko$-characteristic classes for representations, with the Pontrjagin classes of quaternionic representations being the most important. Building on the general results, and their previous calculations, the authors spend the bulk of the book giving a large number of detailed calculations for specific groups (cyclic, quaternion, dihedral, $A_4$, and elementary abelian 2-groups). The calculations illustrate the richness of the theory and suggest many further lines of investigation. They have been applied in the verification of the Gromov-Lawson-Rosenberg conjecture for several new classes of finite groups.|This book is about equivariant real and complex topological $K$-theory for finite groups. Its main focus is on the study of real connective $K$-theory including $ko^*(BG)$ as a ring and $ko_*(BG)$ as a module over it. In the course of their study the authors define equivariant versions of connective $KO$-theory and connective $K$-theory with reality, in the sense of Atiyah, which give well-behaved, Noetherian, uncompleted versions of the theory. They prove local cohomology and completion theorems for these theories, giving a means of calculation as well as establishing their formal credentials. In passing from the complex to the real theories in the connective case, the authors describe the known failure of descent and explain how the $\eta$-Bockstein spectral sequence provides an effective substitute. This formal framework allows the authors to give a systematic calculation scheme to quantify the expectation that $ko^*(BG)$ should be a mixture of representation theory and group cohomology. It is characteristic that this starts with $ku^*(BG)$ and then uses the local cohomology theorem and the Bockstein spectral sequence to calculate $ku_*(BG)$, $ko^*(BG)$, and $ko_*(BG)$. To give the skeleton of the answer, the authors provide a theory of $ko$-characteristic classes for representations, with the Pontrjagin classes of quaternionic representations being the most important. Building on the general results, and their previous calculations, the authors spend the bulk of the book giving a large number of detailed calculations for specific groups (cyclic, quaternion, dihedral, $A_4$, and elementary abelian 2-groups). The calculations illustrate the richness of the theory and suggest many further lines of investigation. They have been applied in the verification of the Gromov-Lawson-Rosenberg conjecture for several new classes of finite groups.

Synthesis and Technique in Inorganic Chemistry

by Gregory S. Girolami, Thomas B. Rauchfuss, Robert J. Angelici

1999 · University Science Books

Previously by Angelici, this laboratory manual for an upper-level undergraduate or graduate course in inorganic synthesis has for many years been the standard in the field. In this newly revised third edition, the manual has been extensively updated to reflect new developments in inorganic chemistry. Twenty-three experiments are divided into five sections: solid state chemistry, main group chemistry, coordination chemistry, organometallic chemistry, and bioinorganic chemistry. The included experiments are safe, have been thoroughly tested to ensure reproducibility, are illustrative of modern issues in inorganic chemistry, and are capable of being performed in one or two laboratory periods of three or four hours. Because facilities vary from school to school, the authors have included a broad range of experiments to help provide a meaningful course in almost any academic setting. Each clearly written & illustrated experiment begins with an introduction that hig! hlights the theme of the experiment, often including a discussion of a particular characterization method that will be used, followed by the experimental procedure, a set of problems, a listing of suggested Independent Studies, and literature references.

Lectures on Vector Bundles Over Riemann Surfaces

by Robert C. Gunning

1967 · Princeton University Press

The description for this book, Lectures on Vector Bundles over Riemann Surfaces. (MN-6), Volume 6, will be forthcoming.