Continue reading “A short rant about power cables in Norway”
A note on torsion in K-theory
In this post we will look at the correspondence between torsion in cohomology of finite CW-complexes and torsion in their K-theory. The title could just as well have been “a use case for Atiyah-Hirzebruch spectral sequence” as this will be our primary tool.
Continue reading “A note on torsion in K-theory”A rant about scooters…
This highly non mathematical post was written during a period of intense fog in Trieste, in northern Italy.
Continue reading “A rant about scooters…”Extending the bump function of irregular geodesic rays to the Karpelevich compactification
In this very short post, we look at the properties of a certain bump function of the collection of all geodesic rays emanating from a fixed point 
towards irregular points on the geodesic boundary 
of a non-compact symmetric space
Notes on polar coordinates for symmetric spaces
In this short blog post, we are going to introduce a “coordinate system” on Riemannian symmetric spaces called polar coordinates, that arise as an immediate consequence of Cartan’s decomposition theorem. The quotation marks are due to the fact that we have some choice in how to express a point in these coordinates.
Continue reading “Notes on polar coordinates for symmetric spaces”Homomorphisms of transformation group C*-algebras – A worked example
In this blog post we work through some examples of computations with crossed product C*-algebras, particularly we look at characterizing *-homomorphisms from a transformation group C*-algebra to a commutative C*-algebra. Some familiarity with C*-crossed products will be assume. Trying to determine all homomorphisms between two given C*-algebra, their algebraic structure, their homotopy classes and so forth, can be quite challenging in general. Most of the standard references on crossed products show how to construct a *-homomorphism of crossed products from an equivariant *-homomorphism of the underlying C*-algebra, but rarely show examples of morphisms that don’t arise in this way.
Continue reading “Homomorphisms of transformation group C*-algebras – A worked example”