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

By Max Karoubi

AT-theory used to be brought via A. Grothendieck in his formula of the Riemann- Roch theorem (cf. Borel and Serre [2]). for every projective algebraic kind, Grothendieck built a bunch 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 truly is this ''topological J^-theory" that this e-book will research. Topological ^-theory has turn into an enormous device in topology. utilizing- idea, Adams and Atiyah have been in a position to provide an easy facts that the one spheres that are supplied with //-space buildings are S^, S^ and S'^. furthermore, it really is attainable to derive a considerable a part of reliable homotopy thought from A^-theory (cf. J. F. Adams [2]). extra purposes to research and algebra are present in the paintings of Atiyah-Singer [2], Bass [1], Quillen [1], and others. A key consider those purposes is Bott periodicity (Bott [2]). the aim of this publication is to supply complicated scholars and mathematicians in different fields with the basic fabric during this topic. furthermore, a number of purposes of the kind defined above are incorporated. normally we've got attempted to make this e-book self-contained, starting with ordinary ideas at any place attainable; notwithstanding, we imagine that the reader understands the elemental definitions of homotopy conception: homotopy sessions of maps and homotopy teams (cf.

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