Local Contributions to Global Deformations of Surfaces.
We shall prove that the moduli space of irreducible Lie algebroid connections over a connected compact manifold has a natural structure of a locally Hausdorff Hilbert manifold. This generalizes some known results for the moduli space of simple semi-connections on a complex vector bundle over a compact complex manifold.
A new formula is established for the asymptotic expansion of a matrix integral with values in a finite-dimensional von Neumann algebra in terms of graphs on surfaces which are orientable or non-orientable.