Joey van der Leer Duran, University of Toronto
"Hodge decompositions for Lie algebroids on manifolds with boundary"
The exterior derivative on a compact manifold with boundary always admits a Hodge decomposition (Conner 1956). In contrast, for the delbar operator on a complex manifold we need the boundary to be convex in order to obtain a Hodge decomposition (Kohn 1964). In this talk we will incorporate these two results into the framework of so-called Lie algebroids. After defining the notions of Cauchy-Riemann structure and q-convexity in this context, we will state a theorem about Hodge decompositions for Lie algebroids that generalizes the cases of the exterior derivative and the delbar operator. As an application, we will discuss a proof of the Newlander-Nirenberg theorem that is based on the Moser trick.
MC 5403