Download E-books K-Theory: An Introduction (Classics in Mathematics) PDF

By Max Karoubi

AT-theory was once brought by way of A. Grothendieck in his formula of the Riemann- Roch theorem (cf. Borel and Serre [2]). for every projective algebraic style, Grothendieck developed a gaggle from the class of coherent algebraic sheaves, and confirmed that it had many great houses. Atiyah and Hirzebruch [3] con­ sidered a topological analog outlined for any compact house X, a gaggle K{X) made from the class of vector bundles on X. it's this ''topological J^-theory" that this ebook will learn. Topological ^-theory has turn into an immense software in topology. utilizing- concept, Adams and Atiyah have been capable of supply an easy evidence that the one spheres that are supplied with //-space buildings are S^, S^ and S'^. additionally, it truly is attainable to derive a considerable a part of solid homotopy conception from A^-theory (cf. J. F. Adams [2]). extra functions to research and algebra are present in the paintings of Atiyah-Singer [2], Bass [1], Quillen [1], and others. A key think about those functions is Bott periodicity (Bott [2]). the aim of this ebook is to supply complicated scholars and mathematicians in different fields with the elemental fabric during this topic. additionally, numerous functions of the sort defined above are incorporated. often we now have attempted to make this ebook self-contained, starting with easy innovations anywhere attainable; although, we suppose that the reader knows the fundamental definitions of homotopy thought: homotopy sessions of maps and homotopy teams (cf.

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