14 citations · 47 across the 28 of their papers we have counts for
16 papers · 1 filter
Bordisms and unbounded -theory
Robin J. Deeley, Magnus Goffeng, Bram Mesland
This monograph studies -theory in its unbounded model. The central object is the -bordism group obtained by imposing the -bordism relation on unbounded -cycles. In…
The rational HK-conjecture: transformation groupoids and a revised version
Robin J. Deeley, Rufus Willett
We prove the rational HK-conjecture for a large class of transformation groupoids in the case when the relevant action has torsion-free stabilizers. A revised version of the ration…
Invariants for the Smale space associated to an expanding endomorphism of a flat manifold
Rachel Chaiser, Maeve Coates-Welsh, Robin J. Deeley +7
We study invariants associated to Smale spaces obtained from an expanding endomorphism on a (closed connected Riemannian) flat manifold. Specifically, the relevant invariants are t…
A counterexample to the HK-conjecture that is principal
Robin J. Deeley
Scarparo has constructed counterexamples to Matui's HK-conjecture. These counterexample and other known counterexamples are essentially principal but not principal. In the present…
Relative geometric assembly and mapping cones, Part II: Chern characters and the Novikov property
Robin J. Deeley, Magnus Goffeng
We study Chern characters and the assembly mapping for free actions using the framework of geometric -homology. The focus is on the relative groups associated with a group homom…
Relative geometric assembly and mapping cones, Part I: The geometric model and applications
Robin J. Deeley, Magnus Goffeng
Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric -homology. The properties of the geometric assembly map are stu…
The bordism group of unbounded KK-cycles
Robin J. Deeley, Magnus Goffeng, Bram Mesland
We consider Hilsum's notion of bordism as an equivalence relation on unbounded -cycles and study the equivalence classes. Upon fixing two -algebras, and a -subalgebra d…
Realizing the analytic surgery group of Higson and Roe geometrically, Part III: Higher invariants
Robin Deeley, Magnus Goffeng
We construct an isomorphism between the geometric model and Higson-Roe's analytic surgery group, reconciling the constructions in the previous papers in the series on "Realizing th…
Realizing the analytic surgery group of Higson and Roe geometrically, Part II: Relative eta-invariants
Robin Deeley, Magnus Goffeng
We apply the geometric analog of the analytic surgery group of Higson and Roe to the relative -invariant. In particular, by solving a Baum-Douglas type index problem, we give a…
Index theory for manifolds with Baas-Sullivan singularities
Robin J. Deeley
We study index theory for manifolds with Baas-Sullivan singularities using geometric K-homology with coefficients in a unital C*-algebra. In particular, we define a natural analog…
Realizing the analytic surgery group of Higson and Roe geometrically, Part I: The geometric model
Robin Deeley, Magnus Goffeng
We construct a geometric analog of the analytic surgery group of Higson and Roe for the assembly mapping for free actions of a group with values in a Banach algebra completion of t…
Analytic and topological index maps with values in the K-theory of mapping cones
Robin J. Deeley
Index maps taking values in the -theory of a mapping cone are defined and discussed. The resulting index theorem can be viewed in analogy with the Freed-Melrose index theorem. T…
Applying geometric K-cycles to fractional indices
Robin J. Deeley, Magnus Goffeng
A geometric model for twisted -homology is introduced. It is modeled after the Mathai-Melrose-Singer fractional analytic index theorem in the same way as the Baum-Douglas model…
R/Z-valued index theory via geometric K-homology
Robin J. Deeley
A model of K-homology with coefficients in a mapping cone using the framework of the geometric cycles of Baum and Douglas is developed. In particular, this leads to a geometric rea…
Geometric -homology with coefficients II
Robin J. Deeley
We discuss the analytic aspects of the geometric model for -homology with coefficients in constructed in "Geometric K-homology with coefficients I". In…
Geometric K-homology with coefficients I
Robin J. Deeley
We construct a Baum-Douglas type model for -homology with coefficients in . The basic geometric object in a cycle is a -…