K-Theory

From the Preface: K -theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch  con­sidered a topological analog defined for any compact space X , a group K{X) constructed from the category of vector bundles on X. It is this ''topological K -theory" that this book will study