## UNPUBLISHED PAPERS

Here are some manuscripts that for one reason on another have remained unpublished. Mostly they have been superseded by other published papers, but since I’m occasionally asked about them anyway I’ve made them available here.

Weyl's theorem and Levinson's theorem (after Kodaira)

These are notes from two 2020 Noncommutative Geometry Seminars at Penn State. The goal in the seminars was to describe and prove theorems of Weyl, Heisenberg and Levinson about Sturm-Liouville operators on a half-line, at least in simple special cases, following an approach due to Kodaira.

Index theory

(With Erik van Erp.) Lectures given at IMPAN in 2016.

Lectures on the index theorem

(With John Roe.) 2008 draft of a book that was never published.

Groupoids, C*-algebras and index theory

From a lectures given at ETHZ in 2004

Counterexamples to the coarse Baum-Connes conjecture

This 1999 paper constructs a counterexample to the coarse Baum-Connes conjecture using expander graphs. The published version of the counterexamples (written with Vincent Lafforgue and Georges Skandalis) focuses on groupoids and uses a somewhat different approach.

Expanders, uniform embeddings and exact C*-algebras

These 1999 notes sketch the relationship between expander graphs and exactness of the C*-algebras of coarse spaces.

Almost homomorphisms and KK-theory

These 1990 notes introduce the notion of almost homomorphism (a.k.a. asymptotic morphism). This is joint work with Alain Connes; an account of it was later published in a Comptes Rendus note authored by the two of us.

K-homology and operators on non-compact manifolds

The purpose of this 1989 article is to develop in detail the main theme of the Atiyah/Kasparov approach to K-homology: that elliptic operators determine K-homology classes, in roughly the same sense that closed, oriented manifolds determine classes in ordinary homology, or closed differential forms determine classes in ordinary co-homology. The most significant aspect of the paper is our concern, throughout, with operators on general, open manifolds.

Weyl's theorem and Levinson's theorem (after Kodaira)

These are notes from two 2020 Noncommutative Geometry Seminars at Penn State. The goal in the seminars was to describe and prove theorems of Weyl, Heisenberg and Levinson about Sturm-Liouville operators on a half-line, at least in simple special cases, following an approach due to Kodaira.

Index theory

(With Erik van Erp.) Lectures given at IMPAN in 2016.

Lectures on the index theorem

(With John Roe.) 2008 draft of a book that was never published.

Groupoids, C*-algebras and index theory

From a lectures given at ETHZ in 2004

Counterexamples to the coarse Baum-Connes conjecture

This 1999 paper constructs a counterexample to the coarse Baum-Connes conjecture using expander graphs. The published version of the counterexamples (written with Vincent Lafforgue and Georges Skandalis) focuses on groupoids and uses a somewhat different approach.

Expanders, uniform embeddings and exact C*-algebras

These 1999 notes sketch the relationship between expander graphs and exactness of the C*-algebras of coarse spaces.

Almost homomorphisms and KK-theory

These 1990 notes introduce the notion of almost homomorphism (a.k.a. asymptotic morphism). This is joint work with Alain Connes; an account of it was later published in a Comptes Rendus note authored by the two of us.

K-homology and operators on non-compact manifolds

The purpose of this 1989 article is to develop in detail the main theme of the Atiyah/Kasparov approach to K-homology: that elliptic operators determine K-homology classes, in roughly the same sense that closed, oriented manifolds determine classes in ordinary homology, or closed differential forms determine classes in ordinary co-homology. The most significant aspect of the paper is our concern, throughout, with operators on general, open manifolds.