5 papers
A secondary pairing between K-theory and K-homology, relative eta invariants, and zeta maps
Rufus Willett
The -homology groups of a -algebra are receptacles for information from topology, operator algebra theory, and representation theory. For applications, one often wants to k…
Conditional representation stability, classification of -homomorphisms, and relative eta invariants
Rufus Willett
A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work o…
The Local Lifting Property, Property FD, and stability of approximate representations
Francesco Fournier-Facio, Rufus Willett
We establish Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for classes of finitely generated groups of central importance in geometric and combinatorial gro…
A trace pairing and Elliott invariant for groupoid homology
Robin Deeley, Rufus Willett
For an étale groupoid, we define a pairing between the Crainic-Moerdijk groupoid homology and the simplex of invariant Borel probability measures on the base space. The main novel…
Controlled KK-theory, and a Milnor exact sequence
Rufus Willett, Guoliang Yu
We introduce controlled -theory groups associated to a pair of separable -algebras. Roughly, these consist of elements of the usual -theory group that…