98 citations · 341 across the 35 of their papers we have counts for
14 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 odd spectral localiser via asymptotic morphisms and quasi-projections
Yuezhao Li, Bram Mesland
We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spe…
Homotopy equivalence in unbounded KK-theory
Koen van den Dungen, Bram Mesland
We propose a new notion of unbounded -cycle, mildly generalising unbounded Kasparov modules, for which the direct sum is well-defined. To a pair of -unital …
Untwisting twisted spectral triples
Magnus Goffeng, Bram Mesland, Adam Rennie
We examine the index data associated to twisted spectral triples and higher order spectral triples. In particular, we show that a Lipschitz regular twisted spectral triple can alwa…
Hecke operators in KK-theory and the K-homology of Bianchi groups
Bram Mesland, Mehmet Haluk Sengun
Let be a torsion-free arithmetic group acting on its associated global symmetric space . Assume that is of non-compact type and let act on the geodesic boundary $\pa…
Boundaries, spectral triples and K-homology
Iain Forsyth, Magnus Goffeng, Bram Mesland +1
This paper extends the notion of a spectral triple to a relative spectral triple, an unbounded analogue of a relative Fredholm module for an ideal . Examples incl…
Shift tail equivalence and an unbounded representative of the Cuntz-Pimsner extension
Magnus Goffeng, Bram Mesland, Adam Rennie
We show how the fine structure in shift-tail equivalence, appearing in the noncommutative geometry of Cuntz-Krieger algebras developed by the first two authors, has an analogue in…
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…
Spectral triples and finite summability on Cuntz-Krieger algebras
Magnus Goffeng, Bram Mesland
We produce a variety of odd bounded Fredholm modules and odd spectral triples on Cuntz-Krieger algebras by means of realizing these algebras as "the algebra of functions on a non-c…
Dense domains, symmetric operators and spectral triples
I. Forsyth, B. Mesland, A. Rennie
This article is about erroneous attempts to weaken the standard definition of unbounded Kasparov module (or spectral triple). We present counterexamples to claims in the literature…
Gauge Theory for Spectral Triples and the Unbounded Kasparov Product
Simon Brain, Bram Mesland, Walter D. van Suijlekom
We explore factorizations of noncommutative Riemannian spin geometries over commutative base manifolds in unbounded KK-theory. After setting up the general formalism of unbounded K…
Spectral triples and KK-theory: A survey
Bram Mesland
This survey deals with the construction of a category of spectral triples that is compatible with the Kasparov product in -theory. These notes serve as an intuitive guide to th…
Groupoid cocycles and K-theory
Bram Mesland
Let be a cocycle on a locally compact Hausdorff groupoid with Haar system. Under some mild conditions (satisfied by all integer valued cocycles o…
Unbounded bivariant -theory and correspondences in noncommutative geometry
Bram Mesland
By introducing a notion of smooth connection for unbounded -cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order…