Gauge theory for spectral triples and the unbounded Kasparov product
We explore factorizations of noncommutative Riemannian spin geometries over
commutative base manifolds in unbounded KK-theory. After setting up the general formalism …
commutative base manifolds in unbounded KK-theory. After setting up the general formalism …
[HTML][HTML] Nonunital spectral triples and metric completeness in unbounded KK-theory
We consider the general properties of bounded approximate units in non-self-adjoint
operator algebras. Such algebras arise naturally from the differential structure of spectral …
operator algebras. Such algebras arise naturally from the differential structure of spectral …
Operator ‐correspondences in analysis and geometry
An operator∗‐algebra is a non‐self‐adjoint operator algebra with completely isometric
involution. We show that any operator∗‐algebra admits a faithful representation on a Hilbert …
involution. We show that any operator∗‐algebra admits a faithful representation on a Hilbert …
Differentiable absorption of Hilbert -modules, connections, and lifts of unbounded operators
J Kaad - Journal of Noncommutative Geometry, 2017 - ems.press
The Kasparov absorption (or stabilization) theorem states that any countably generated
Hilbert C-module is isomorphic to a direct summand in the standard module of square …
Hilbert C-module is isomorphic to a direct summand in the standard module of square …
Index theory of uniform pseudodifferential operators
A Engel - arxiv preprint arxiv:1502.00494, 2015 - arxiv.org
We generalize Roe's index theorem for graded generalized Dirac operators on amenable
manifolds to multigraded elliptic uniform pseudodifferential operators. This generalization …
manifolds to multigraded elliptic uniform pseudodifferential operators. This generalization …
Indices of pseudodifferential operators on open manifolds
A Engel - arxiv preprint arxiv:1410.8030, 2014 - arxiv.org
We generalize Roe's Index Theorem for operators of Dirac type on open manifolds to elliptic
pseudodifferential operators. To this end we introduce a class of pseudodifferential …
pseudodifferential operators. To this end we introduce a class of pseudodifferential …
The unbounded Kasparov product by a differentiable module
J Kaad - arxiv preprint arxiv:1509.09063, 2015 - arxiv.org
In this paper we investigate the unbounded Kasparov product between a differentiable
module and an unbounded cycle of a very general kind that includes all unbounded …
module and an unbounded cycle of a very general kind that includes all unbounded …
Morita invariance of unbounded bivariant K-theory
J Kaad - arxiv preprint arxiv:1612.08405, 2016 - arxiv.org
We introduce a notion of Morita equivalence for non-selfadjoint operator algebras equipped
with a completely isometric involution (operator*-algebras). We then show that the …
with a completely isometric involution (operator*-algebras). We then show that the …
[HTML][HTML] Uniform K-theory, and Poincaré duality for uniform K-homology
A Engel - Journal of Functional Analysis, 2019 - Elsevier
We revisit Špakula's uniform K-homology, construct the external product for it and use this to
deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on …
deduce homotopy invariance of uniform K-homology. We define uniform K-theory and on …
The unbounded Kasparov product by a differentiable module
J Kaad - Journal of Noncommutative Geometry, 2021 - ems.press
In this paper we investigate the unbounded Kasparov product between a differentiable
module and an unbounded cycle of a very general kind that includes all unbounded …
module and an unbounded cycle of a very general kind that includes all unbounded …