Marco Zambon (UAM), 

Higher Dirac structures
 


                        We introduce a geometric notion which generalizes both Dirac
                        structures and closed forms of arbitrary degree. One motivation for
                        them is that they are equivalent to the MultiDirac structures that
                        recently appeared in field theory, but are simpler to handle. Our main
                        motivation is that the "observables" associated to Higher Dirac
                        structure form a homotopy Lie algebra, generalizing the fact that
                        functions on a symplectic manifold are endowed with a Poisson bracket.
                        As an application we show that any connected, compact, orientable
                        manifold has a canonically associated homotopy Lie algebra.