Noncommutative Riemannian spin geometry from a bundle theoretic point of view
Välkommen till föreläsningen i seminarieserien i matematik.
Riemannian spin geometry is a special and important topic within differential geometry which is mainly based on principal bundle theory and has objects such as spin structures and Dirac operators. It also has wide applications to mathematical physics, in particular to quantum field theory, where spin structures are an essential ingredient in the definition of any theory with uncharged fermions. In the noncommutative setting the notion of a spectral triple provides a natural framework for noncommutative Riemannian spin geometry. However, unlike in the classical setting, the axiomatic description of a on commutative Riemannian spin geometry does not incorporate noncommutative principal bundles, which are becoming increasingly prevalent in various applications of geometry and mathematical physics. In this talk we give an introduction to the subject as well as a novel perspective via noncommutative principal bundles.