Mykola Matviichuk, University of Toronto
"Deformation of Dirac structures via L infinity algebras"
Dirac structures are a common generalization of Poisson brackets, presymplectic structures, foliations and complex structures. Classically, to describe the deformation theory of a Dirac structure L inside a Courant algebroid C, one makes an auxiliary choice of a transverse Dirac structure. This choice allows to write down a certain differential graded Lie algebra (dgla, for short), whose Maurer-Cartan elements represent the deformatoins of L. Inconveniently, the obtained dgla is NOT independent on the choice of the transverse Dirac structure. We prove, however, that the dgla's coming from two different choices of the transverse Dirac structure are canonically isomorphic in the category of L infinity algebras (a.k.a. dgla's up to homotopy). The L infinity isomorphism has an explicit formula, which allows to calculate the L infinity transport of the Maurer-Cartan elements. The talk is based on the preprint (joint with M. Gualtieri and G. Scott) https://arxiv.org/pdf/1702.08837.pdf
MC 5403