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Universal isomonodromic deformations of meromorphic rank 2 connections on curves

Viktoria Heu (2010)

Annales de l’institut Fourier

We consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby more elementary than the construction in arbitrary rank due to B. Malgrange and I. Krichever and it includes...

Universal lifting theorem and quasi-Poisson groupoids

David Inglesias-Ponte, Camille Laurent-Gengoux, Ping Xu (2012)

Journal of the European Mathematical Society

We prove the universal lifting theorem: for an α -simply connected and α -connected Lie groupoid Γ with Lie algebroid A , the graded Lie algebra of multi-differentials on A is isomorphic to that of multiplicative multi-vector fields on Γ . As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases. The second goal of the paper is the study of basic properties of quasi-Poisson groupoids. In particular,...

Universal prolongation of linear partial differential equations on filtered manifolds

Katharina Neusser (2009)

Archivum Mathematicum

The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately to obstructions to the existence of solutions. Moreover, we will deduce that the solution space of such equations is always finite dimensional.

Universal spaces for manifolds equipped with an integral closed k -form

Hông-Vân Lê (2007)

Archivum Mathematicum

In this note we prove that any integral closed k -form φ k , k 3 , on a m-dimensional manifold M m , m k , is the restriction of a universal closed k -form h k on a universal manifold U d ( m , k ) as a result of an embedding of M m to U d ( m , k ) .

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