B. Burgstaller

activity

20242026

collaborators

4 papers

math.KT2026

The universal property of graded $K K^{G}$ -theory

Bernhard Burgstaller

A universal category-theoretical characterization of groupoid equivariant $K K^{G}$ -theory for $Z_{2}$ -graded $C^{*}$ -algebras is established, by observing the `` $K K$ -axiom'' t…

math.KT2025

Computing the $K$ -homology $K$ -theory product in splitexact algebraic $K K$ -theory

Bernhard Burgstaller

Explicit formulas are indicated that compute the product $z \cdot w$ of a level-one element $z \in K K^{G} (A, C)$ and any element $w \in K K^{G} (C, B)$ in splitexact algebraic…

math.KT2025

Corner embeddings into algebras of compact operators in $K$ -theory

Bernhard Burgstaller

We show that in $K$ -theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK…

math.KT2024

On the $K$ -theory in splitexact algebraic $K K$ -theory

Bernhard Burgstaller

It is proven that in the universal splitexact equivariant algebraic $K K$ -theory for algebras, the $K$ -theory groups coincide with classical $K$ -theory in the sense of Phillips. Thi…

The universal property of graded KKG-theory

Computing the K-homology K-theory product in splitexact algebraic KK-theory

Corner embeddings into algebras of compact operators in K-theory

On the K-theory in splitexact algebraic KK-theory

The universal property of graded $K K^{G}$ -theory

Computing the $K$ -homology $K$ -theory product in splitexact algebraic $K K$ -theory

Corner embeddings into algebras of compact operators in $K$ -theory

On the $K$ -theory in splitexact algebraic $K K$ -theory