ATtheory was introduced by A. Grothendieck in his formulation of the Riemann Roch theorem (cf. Borel and Serre [2]). 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 [3] con sidered 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 J^theory" that this book will study. Topological ^theory has become an important tool in topology. Using theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with //space structures are S^, S^ and S'^. Moreover, it is possible to derive a substantial part of stable homotopy theory from A^theory (cf. J. F. Adams [2]). Further applications to analysis and algebra are found in the work of AtiyahSinger [2], Bass [1], Quillen [1], and others. A key factor in these applications is Bott periodicity (Bott [2]). 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 selfcontained, 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 (cf.
About Max Karoubi
Max Karoubi received his PhD in mathematics (Doctorat d'Etat) from Paris University in 1967, while working in the CNRS (Centre National de la Recherche Scientifique), under the supervision of Henri Cartan and Alexander Grothendieck. After his PhD, he took a position of "Maitre de Conferences" at the University of Strasbourg until 1972. He was then nominated full Professor at the University of Paris 7Denis Diderot until 2007. He is now an Emeritus Professor there.Details Book
Author  :  Max Karoubi 
Publisher  :  SpringerVerlag Berlin and Heidelberg GmbH 
Data Published  :  20 August 2008 
ISBN  :  3540798897 
EAN  :  9783540798897 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  316 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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