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 I have posted two unpublished essays which are not on the arXiv, plus some talk slides.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.

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.

Essays

Where Mathematics Comes From (Book Review)

Mathematics vs. the Law

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)

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