Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606006 | Differential Geometry and its Applications | 2015 | 19 Pages |
I define higher codimensional versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures. Cartan distributions on jet spaces provide canonical examples. More generally, I define higher codimensional versions of pre-contact structures as distributions on manifolds whose characteristic symmetries span a constant dimensional distribution. I call them pre-multicontact structures. Every distribution is almost everywhere, locally, a pre-multicontact structure. After showing that the standard symplectization of contact manifolds generalizes naturally to a (pre-)multisymplectization of (pre-)multicontact manifolds, I make use of results by C. Rogers and M. Zambon to associate a canonical L∞L∞-algebra to any (pre-)multicontact structure. Such L∞L∞-algebra is a multicontact version of the Jacobi bracket on a contact manifold. Unlike the multisymplectic L∞L∞-algebra of Rogers and Zambon, the multicontact L∞L∞-algebra is always a homological resolution of a Lie algebra. Finally, I describe in local coordinates the L∞L∞-algebra associated to the Cartan distribution on jet spaces.