Z_2^n-manifolds: Recent advances and ongoing work

par Andrew J. Bruce (University of Luxembourg)

vendredi 21 sept. 2018, 14:00 → 15:00 Europe/Paris

112 (Institut Camille Jordan)

A locally ringed space approach to coloured supermanifolds was recently initiated by Grabowski and Poncin together with a collection of collaborators.  We must comment that the theory, while a natural extension of the theory of supermanifolds, is not always straightforward nor trivial. While the basic ideas are now in place, we will report on some recent developments regarding the nuclear Frechet algebra structure of the structure sheaf and the continuity of morphisms between Z_2^n-manifolds. These results allow us, for example,  to reconstruct the structure sheaf from knowing the algebra of global functions and to construct the Cartesian product of two  Z_2^n-manifolds. Given time, we will also point towards further problems we would like to understand and hopefully such advances will prove useful in physics.