# Topological Homology Research

Our group is particularly interested in the cohomological problems that arise in noncommutative geometry.

## About topological homology

Topological homology concerns questions on the structure and properties of Banach and C*-algebras. Mainly it describes their properties from the viewpoint of homological algebra.

We are particularly interested in the cohomological problems that arise in noncommutative geometry. An example of this is the calculation of cyclic type cohomology of topological algebras.

The theory has applications in many branches of mathematics, including:

- spectral theory
- the theory of de Rham homology in differential geometry automatic continuity theory
- K-theory