Marco Zambon

Simultaneous deformations and Poisson geometry

We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an

Coisotropic embeddings in Poisson manifolds

L_{\infty }

Spin(7)-manifolds in compactifications to four dimensions

-algebra, which we construct explicitly. Our machinery is based on Voronov’s derived bracket construction. In this paper we consider only geometric applications, including deformations of coisotropic submanifolds in Poisson manifolds, of twisted Poisson structures, and of complex structures within generalized complex geometry. These applications cannot be, to our knowledge, obtained by other methods such as operad theory.

L∞-algebra actions

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, which is naturally endowed with a Poisson structure. Then we give conditions under which a Dirac manifold can be embedded coisotropically in a Poisson manifold, extending a classical theorem of Gotay.

An Extension of the Marsden-Ratiu Reduction for Poisson Manifolds

A bstractWe describe off-shell N=1

Deformations of Coisotropic Submanifolds for Fibrewise Entire Poisson Structures

\mathcal{N}=1

L-infinity-algebra actions

M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological Spin(7)-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold ℳ8