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K-Theory for Operator Algebras

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View other formats and editions. K -Theory has revolutionized the study of operator algebras in the last few years.

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As a result, many topolo- gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability.

While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form. It is the ambitious goal of these notes to fill this gap.

We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text. Since its inception in the early s, the field has grown rapidly, until a deep and elaborate machinery has evolved. This book is the first to consolidate this material and does an excellent job of presenting the path of least resistance to the key results while keeping the reader informed about the many important sidetracks.

Operator Algebra Resources

European Maths Society Journal. Added to basket. The Shape of Space. Jeffrey R.

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Fractal Geometry. Kenneth Falconer. Edwin Abbott Abbott. Operator K-theory resembles topological K-theory more than algebraic K-theory. In particular, a Bott periodicity theorem holds. So there are only two K-groups, namely K 0 , which is equal to algebraic K 0 , and K 1. As a consequence of the periodicity theorem, it satisfies excision.

K-Theory for Operator Algebras by Bruce Blackadar (2 star ratings)

Schedule Please see my Google Calendar. Curriculum Vitae.

Introduction to Algebraic K-Theory (Lecture 1)

My portrait: Drawn at the Christmas market in Goettingen, winter The joint spectral flow and localization of the indices of elliptic operators Annals of K-theory, 1 1 , D thesis.