By Max Karoubi

*From the Preface: K*-theory was once brought by means of A. Grothendieck in his formula of the Riemann- Roch theorem. for every projective algebraic type, Grothendieck developed a gaggle from the class of coherent algebraic sheaves, and confirmed that it had many great homes. Atiyah and Hirzebruch considered a topological analog outlined for any compact house *X*, a bunch *K{X)* made from the class of vector bundles on X. it really is this ''topological *K*-theory" that this e-book will study.

*K*-theory has develop into a tremendous device in topology. Using

*K*- concept, Adams and Atiyah have been capable of supply an easy evidence that the one spheres which might be supplied with

*H*-space constructions are S1, S3 and S7. furthermore, it truly is attainable to derive a considerable a part of sturdy homotopy idea from K-theory.

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