K-Theory: An Introduction PDF ePub eBook

Books Info:

K-Theory: An Introduction free pdf AT-theory 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 Atiyah-Singer [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 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 (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 7-Denis Diderot until 2007. He is now an Emeritus Professor there.

Details Book

Author : Max Karoubi
Publisher : Springer-Verlag 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 :

Reviews K-Theory: An Introduction

17 Comments Add a comment

Related eBooks Download

  • Local Homotopy Theory free pdfLocal Homotopy Theory

    This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory..

  • Algebraic Homotopy free pdfAlgebraic Homotopy

    This book gives a general outlook on homotopy theory- fundamental concepts. such as homotopy groups and spectral sequences. are developed from a few axioms and are thus available in a broad variety of contexts..

  • Bordism, Stable Homotopy and Adams Spectral Sequences free pdfBordism, Stable Homotopy and Adams Spectral Sequences

    This book is a compilation of lecture notes that were prepared for the graduate course "Adams Spectral Sequences and Stable Homotopy Theory" given at the Fields Institute during the autumn of 1995..

  • A Topological Introduction to Nonlinear Analysis free pdfA Topological Introduction to Nonlinear Analysis

    -review of the first edition. New to this edition: additional applications of the theory and techniques. as well as several new proofs. This book is ideal for self-study for mathematicians and students interested in geometric and algebraic topology..

  • Sheaves in Geometry and Logic free pdfSheaves in Geometry and Logic

    This book is an introduction to the theory of toposes. as first developed by Grothendieck and later developed by Lawvere and Tierney. Beginning with several illustrative examples. the book explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic..

  • K-Theory: An Introduction free pdfK-Theory: An Introduction

    . AT-theory 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 th