We define the Bohr-Sommerfeld quantization via T-modules for a b-symplectic toric manifold and show that it coincides with the formal geometric quantization of [GMW18b]. In particular, we prove that its dimension is given ...

In this article, we introduce b-semitoric systems as a generalization of semitoric systems, specifically tailored for b-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate ...

In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the ...

Manifolds with boundary, with corners, b-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E-manifolds. E-manifolds were introduced in [NT01] and investigated ...

In this article we generalize a theorem by Palais on the rigidity ofcompact group actions to cotangent lifts. We use this result to prove rigidity forintegrable systems on symplectic manifolds including sytems with ...

In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry ...

(English) In this thesis we study several mathematical objects that are essential to formulate and model physical systems. Applying the tools provided by differential geometry, we develop and analyze different mathematical ...