Topological characterisation of electronic states in spin textures from non-commutative K-theory

For applications in future information technologies materials exhibiting exotic spin textures, such as skyrmions, are in high demand. In order to characterise electronic states in spin textures topological invariants are employed. With the algebraic methods from non-commutative geometry and K-Theory these invariants can be accessed even for aperiodic spin arrangements. This talk will introduce the idea of how to describe topology in algebraic terms and review our recent application to arbitrary multi-q states.