Robin J. Deeley

Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang–Su algebra

The principal aim of this paper is to give a dynamical presentation of the Jiang-Su algebra. Originally constructed as an inductive limit of prime dimension drop algebras, the Jiang-Su algebra has gone from being a poorly understood oddity to having a prominent positive role in George Elliotts classification programme for separable, nuclear C*-algebras. Here, we exhibit an etale equivalence relation whose groupoid C*-algebra is isomorphic to the Jiang-Su algebra. The main ingredient is the construction of minimal homeomorphisms on infinite, compact metric spaces, each having the same cohomology as a point. This construction is also of interest in dynamical systems. Any self-map of an infinite, compact space with the same cohomology as a point has Lefschetz number one. Thus, if such a space were also to satisfy some regularity hypothesis (which our examples do not), then the Lefschetz-Hopf Theorem would imply that it does not admit a minimal homeomorphism.

Analytic and topological index maps with values in the

Index maps taking values in the

K

K

-theory of mapping cones

-theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. The framework of geometric

The bordism group of unbounded KK-cycles

K

Wieler solenoids, Cuntz–Pimsner algebras and K-theory

-homology is used in a fundamental way. In particular, an explicit isomorphism from a geometric model for

A Signed Version of Putnam’s Homology Theory: Lefschetz and Zeta Functions

K

Relative geometric assembly and mapping cones, part I: the geometric model and applications: RELATIVE GEOMETRIC ASSEMBLY AND MAPPING CONES, PART I

-homology with coefficients in a mapping cone,

REALIZING THE ANALYTIC SURGERY GROUP OF HIGSON AND ROE GEOMETRICALLY, PART I: THE GEOMETRIC MODEL

C_{\phi}

R/Z-valued index theory via geometric K-homology

, to