Topology, K. Janich

This book constitutes nothing less than an up-to-date survey of the whole field of topology (with the exception of "general (set-theoretic) topology"), or, in the words of Novikov himself, of what was termed at the end of the 19th century "Analysis Situs", and subsequently diversified into the various subfields of combinatorial, algebraic, differential, homotopic, and geometric topology. The book gives an overview of these subfields, beginning with the elements and proceeding right up to the present frontiers of research.

K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol­ ogy," K -theory has opened vast new vistas within the structure theory of C*­ algebras, as well as leading to profound and unexpected applications of opera­ tor algebras to problems in geometry and topology. As a result, many topolo­ gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

The blowgun is a mysterious tool of silent death. Michael Janich reveals the many secrets of its capabilities and uses: how to buy or make your own blowgun and darts (including "special" projectiles), shoot the weapon, devise custom targets and customize, maintain and store your gun. This is the best book on this fascinating and deadly device.

Authors: Fomenko, Anatoly, Fuchs, Dmitry
Updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand
Presents material concisely but rigorously
Illuminates the subject matter with a range of technical and artistic illustrations, along with a wealth of examples and computations meant to provide a treatment of the topic that is both deep and broad
Contains an entirely new chapter on K-theory and the Riemann-Roch theorem