5 citations · 16 across the 16 of their papers we have counts for
11 papers · 1 filter
The universal property of graded -theory
Bernhard Burgstaller
To each Kasparov cycle we attach inclusions satisfying . A lift of a second factor along therefore re…
Computing the -homology -theory product in splitexact algebraic -theory
Bernhard Burgstaller
Explicit formulas are indicated that compute the product of a level-one element and any element in splitexact algebraic…
Corner embeddings into algebras of compact operators in -theory
Bernhard Burgstaller
We show that in -theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK…
On the -theory in splitexact algebraic -theory
Bernhard Burgstaller
It is proven that in the universal splitexact equivariant algebraic -theory for algebras, the -theory groups coincide with classical -theory in the sense of Phillips. Thi…
A kind of -theory for rings
Bernhard Burgstaller
A group equivariant -theory for rings will be defined and studied in analogy to Kasparov's -theory for -algebras. It is a kind of linearization of the category of ring…
Aspects of equivariant -theory in its generators and relations picture
Bernhard Burgstaller
We give a new proof of the universal property of -theory with respect to stability, homotopy invariance and split-exactness for a locally compact group, or a locally comp…
A note on a certain Baum--Connes map for inverse semigroups
Bernhard Burgstaller
Let denote a countable inverse semigroup. We construct a kind of a Baum--Connes map by a categorial approach via localization…
The generators and relations picture of -theory
Bernhard Burgstaller
This is half an overview article since what we describe here is essentially known. We describe -theory by generators and relations in a formal sum of formal products of -hom…
Inverse semigroup equivariant -theory and -extensions
Bernhard Burgstaller
In this note we extend the classical result by G. G. Kasparov that the Kasparov groups can be identified with the extension groups $\mbox{Ext}(A,B)$ to the inverse semi…
Attempts to define a Baum--Connes map via localization of categories for inverse semigroups
Bernhard Burgstaller
Meyer and Nest showed that the Baum--Connes map is equivalent to a map on -theory of two different crossed products. This approach is strongly categorial in method since its bas…
Equivariant -theory of -discrete groupoids and inverse semigroups
Bernhard Burgstaller
For an -discrete Hausdorff groupoid and an inverse semigroup of slices of there is an isomorphism between -equivariant -theory and compat…