2 edition of **K-theory.** found in the catalog.

K-theory.

Johan Dupont

- 378 Want to read
- 5 Currently reading

Published
**1968**
by Aarhus Universitet in Aarhus
.

Written in English

**Edition Notes**

Lectures, Fall 1968.

Series | Lecture notes series -- No. 11. |

The Physical Object | |
---|---|

Pagination | 115 p. |

Number of Pages | 115 |

ID Numbers | |

Open Library | OL19989055M |

This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory.5/5(3).

This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. K-Theory: An Introduction (Classics in Mathematics series) by Max Karoubi. Digital Rights Management (DRM) The publisher has supplied this book in encrypted form, which means that you need to install free software in order to unlock and read it.

K-theory of Waldhausen categories. In algebra, the S-construction is a construction in algebraic K-theory that produces a model that can be used to define higher K-groups. It is due to Friedhelm Waldhausen and concerns a category with cofibrations and weak equivalences; such a category is called a Waldhausen category and generalizes Quillen's exact category. Book Description. These notes are based on the course of lectures I gave at Harvard in the fall of They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory.

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One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism.5/5(1).

K-Theory, An Introduction is a phenomenally attractive book: a fantastic introduction and then some. serve as a fundamental reference and source of instruction for outsiders who would be fellow travelers."Cited by: Algebraic K-theory describes a branch of algebra that centers about two functors.

K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian by: ``The K-book: an introduction to algebraic K-theory'' by Charles K-theory.

book (Graduate Studies in Math. vol.AMS, ) Errata to the published version of the K-book. Introduction To K theory and Some Applications. K-theory.

book book explains the following topics: Topological K-theory, K-theory of C* algebras, Geometric and Topological Invarients, THE FUNCTORS K1 K2, K1, SK1 of Orders and Group-rings, Higher Algebraic K-theory, Higher Dimensional Class Groups of Orders and Group rings, Higher K-theory of Schemes.

K theory Paperback – January 1, by M F Atiyah (Author) out of 5 stars 1 rating5/5(1). Book Description. K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to K-theory.

book subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the by: From 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. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Introduction This handbook offers a compilation of techniques and results in K-theory. These two volumes consist of chapters, each of which is dedicated to a specific topic and is written by a. K-Theory *immediately available upon purchase as print book shipments may be delayed due to the COVID crisis.

ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra.

One of the features of the treatment is that no use is made of ordinary homology or cohomology theory/5(8). From 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. K-theory - CRC Press Book.

These notes are based on the course of lectures I gave at Harvard in the fall of They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary. Vector Bundles & K-Theory The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes.

Here is a provisional Table of Contents. Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group K 0 of a category and uses explicit algebraic presentations, and higher algebraic K-theory which requires topological or ho- mological machinery to deﬁne.

Introduction To K theory and Some Applications. This book explains the following topics: Topological K-theory, K-theory of C* algebras, Geometric and Topological Invarients, THE FUNCTORS K1 K2, K1, SK1 of Orders and Group-rings, Higher Algebraic K-theory, Higher Dimensional Class Groups of Orders and Group rings, Higher K-theory of Schemes, Mod-m.

K-theory. DOI link for K-theory. K-theory book. K-theory. DOI link for K-theory. K-theory book. By Michael Atiyah. Edition 1st Edition. First Published In fact, rational cohomology is defined in terms of theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism.

In Book Edition: 1st Edition. In closing, then, K-Theory, An Introduction is a phenomenally attractive book: a fantastic introduction and then some. Only a master like Karoubi could have written the book, and it will continue to be responsible for many seductions of fledglings to the ranks of topological K-theorists as well as serve as a fundamental reference and source of.

K-THEORY. An elementary introduction by Max Karoubi Clay Mathematics Academy The purpose of these notes is to give a feeling of “K-theory”, a new interdisciplinary subject within Mathematics.

This theory was invented by Alexander Grothendieck1 [BS] in the 50’s. In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory.

It is also a fundamental tool in the field of operator algebras. This book is both an introduction to K-theory and a text in algebra. These two roles are entirely compatible. On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the clasical algebraic K-theory.4/5(1).An elementary introduction by Max Karoubi Conference at the Clay Mathematics Research Academy The purpose of these notes is to give a feeling of “K-theory”, a new interdisciplinary subject within Mathematics.

This theory was invented by Alexander Grothendieck1 [BS] in .