Mathematics Publications

Below are links to PDF copies of my books (click on the titles). I have not included copies of my research papers since the ones I have digital copies of are all posted on the arXiv. I have posted a few unpublished essays which are not on the arXiv, plus some talk slides. All these files are downloadable. They are all copyright by the author, and may be used according to the Creative Commons rules with proper attribution.

Books

K-Theory for Operator Algebras

MSRI Series. First edition 1986 (Springer-Verlag), Second Edition 1998 (Cambridge University Press). The version here is a slightly corrected second edition.

Operator Algebras

Encyclopedia of Mathematics, Springer-Verlag, 2005. The version here is revised and corrected, with hyperlinks added for ease of navigation. An errata is available for the published edition.

Classification of C*-Algebras

This is an incomplete draft of a book on the classification of simple nuclear C*-algebras. The book project has stagnated (hopefully temporarily!), so I decided to post the manuscript as it is now in the hopes it will be useful and elicit comments. Some sections are still rough, and there are undoubtedly errors and misstatements. The principal missing things are (1) The proof of the classification theorem (!) (2) A better and more complete description of the nonunital case (3) An exposition of the general construction of examples (although many examples are described). I have included a chapter on semiprojectivity in the hopes that it will be relevant for classification, but this chapter will probably not appear in the final version unless I or someone else proves some substantial additional results. Comments invited!

Real Analysis

This large online manuscript is still a work in progress. I estimate it is roughly 3/4 "finished" (although I will probably never regard it as truly finished!) I still regularly revise it (the additions and revisions are usually rather slight), and up-to-date versions will be posted here. The manuscript is not yet organized as I envision it, as sort of a mini-Wikipedia. (I do not have the technical expertise to do this, and if anyone wants to help me with this it would be most welcome!) In the meantime, I recommend that the file be downloaded or viewed in Preview, to facilitate navigation.

Ring Theory

I'm not the only Bruce Blackadar. There was another, a distant cousin (now deceased). I never met him. Check this link, beginning at 3:08.

Essays

Where Mathematics Comes From (Book Review)

I may have gotten too worked up here over a book which probably doesn't deserve it, but it has gotten shockingly positive testimonials from some people who should know better.

Mathematics vs. the Law

This essay seems a little out of date now with the outrages of the current administration and the assault on the rule of law.

The Asylum of Doctor Tarr and Professor Fether

This is a logic puzzle, adapted from The Lady or the Tiger? by Raymond Smullyan, which I used to give to my students. Click here for the solution.

Slides

Here are slides from some talks I have given in recent years.

Classification of C*-Algebras

Nuclearity, Quasidiagonality, and Generalized Inductive Limits

Scaling Elements Revisited (2000)

The Algebraization of Dynamics (2003)

Nonstable K-Theory for Free Products (2007)

Does Bivariant K-Theory See Complex Structure? (2008)

Ideal Structure of NF Algebras and the UCT Revisited (2008)

C*-Algebras Generated by Arrays of Projections (2008)

Fun With Continued Fractions (2009)

Semiprojectivity: A Retrospective (2010)

Recent Results on Semiprojectivity (2011)

Noncommutative PL-Topology (2011)

The Homotopy Lifting Theorem (2012)

Homotopies and Liftings (2012)

Lifting Commutation Relations in Cuntz Algebras (2015)

What Does "Obvious" Mean in Mathematics? (And why do we have to prove things?) (2015)

Classification of Simple C*-Algebras (2017)

Symmetry and Complex Structure in C*-Algebras (2017)

Introduction to Noncommutative Topology (2020)

Some Exotic Manifolds: Beyond Algebraic Topology (2021)

Hilbert Spaces Without Countable AC (2023)

Go back to homepage