大象传媒

A is a space where each point is replace by an entire vector space in a nice and continuous manner. Vector bundles and their geometry are important in connection with , however, it appears that finer structures are also of importance. In this connection, Baas (NTNU), Richter (Hamburg), Rognes (UiO) and I have a construction for "2-vector bundles", where vector spaces are exchanged for 2-vector spaces. Just as a vector is a tuple of numbers, a 2-vector is a tuple of vector spaces, and matrices of numbers are exchanged for matrices of vector spaces. The surprise is that this gives rise to a theory connected to quantum field theories and to "the prime factorisation of the ".

A shortcoming in connection with the application to quantum field theory is that the geometry of 2-vector bundles is not developed. This is not a simple question, for example, one does not have a good idea of what curvature should mean, one has no and there is a complete lack of a theory for determinants for 2-vector spaces; and problems in this regard are interesting enough in themselves. Some of the questions will require a bit of differential geometry.