Roughly speaking, Z(2)(n)-manifolds are 'manifolds' equipped with Z(2)(n)-graded commutative coordinates with the sign rule being determined by the scalar product of their Z(2)(n)-degrees. We examine the notion of a symplectic Z(2)(n)-manifold, i.e., a Z(2)(n)-manifold equipped with a symplectic two-form that may carry non-zero Z(2)(n)-degree. We show that the basic notions and results of symplectic geometry generalise to the 'higher graded' setting, including a generalisation of Darboux's theorem.
NSTL
Amer Inst Mathematical Sciences-Aims
