Tepui fibration: Fibrations whose fibers jump dimension and with a notion of smoothnessMPIM

by Alfonso Garmendia (MPIM)

Wednesday Aug 20, 2025, 10:30 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Higher Differential Geometry Seminar

We study smooth maps $p:X->M$ where $M$ is a manifold, $X$ a diffeological space, and the fibers of $p$ are manifolds. On such spaces, we define a tangent functor that enables us to perform differential calculus despite the presence of singularities. Our approach is inspired by the work of Androulidakis and Skandalis, who construct a diffeological groupoid integrating a singular foliation. The source map of this groupoid gives rise to a space of the kind we consider, and our tangent functor allows us to recover the original singular foliation from this structure. We also investigate the notion of vector bundles in this context and establish a generalized version of the Serre–Swan theorem adapted to this singular setting. This is joint work with David Miyamoto and Leonid Ryvkin.