Connes’ theory of spectral triples provides a extension of « geometry » beyond the riemannian setting, to the noncommutative framework.
The generalisation to the pseudo-riemannian case (i.e lorentzian signature) is far from obvious. There exist several attempts to describe pseudo-riemannian manifolds in term of spectral triples, but so far still incomplete. In this talk we will explore an alternative way, consisting in starting with the euclidean signature, and moving to the lorentzian setting thanks to a twist of the spectral triple. On the way, we shall stress an intriguing link between torsion and Wick rotation !
Kilian Hersent
