Non-regular parabolic geometries via the notion of bi-filtered manifolds

Boris Doubrov (BSU)

Sep 10. 2021, 09:30 — 10:30

The aim of this talk is to introduce the notion of bi-filtered manifolds, which are smooth or complex analytic manifolds, whose tangent space is equipped with a descending filtration indexed by lexicographically ordered pairs of integers (i,j)<(0,0) and compatible with the Lie bracket. While being the generalization of a classical notion of filtered manifolds due to Tanaka, this new notion of bi-filtered manifolds provides a uniform approach to studying some non-regular parabolic geometries, which become regular in this new bi-filtered sence. 

We give interpretation of bi-filtered manifolds in terms of cone sturcutres on filtered manifolds, define an alalog of their symbol and its Tanaka prolongation, prove the existence of a natural Cartan connection under the assumption of existence of invariant normalization conditions. As an application, we present several examples of geometric structures that can be effectively treated by this appraoch.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and Q-manifolds (Thematic Programme)
Xavier Bekaert (U of Tours)
Andreas Cap (U of Vienna)
Stefan Fredenhagen (U of Vienna)
Maxim Grigoriev (U of Mons)
Alexei Kotov (U Hradec Králové)