{"product_id":"ktheory-an-introduction-classics-in-mathematics-9783540798897","title":"K-Theory: An Introduction (Classics in Mathematics)","description":"\u003cp\u003eFrom 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 KX) constructed from the category of vector bundles on X. It is this topological K-theory\" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory  Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1  S3 and S7. Moreover  it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition  several applications of the type described above are included. In general we have tried to make this book self-contained  beginning with elementary concepts wherever possible; however  we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a \"generalized cohomology theory\".\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45960413020213,"sku":"ByrdShop_3540798897","price":155.64,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9783540798897.jpg?v=1788286640","url":"https:\/\/atxbooks.com\/products\/ktheory-an-introduction-classics-in-mathematics-9783540798897","provider":"ATX Books","version":"1.0","type":"link"}