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In this work we present different results obtained, in analyzing several aspects of gravity in non commutative space-time. We obtain generalized Euler and Pontrgajin topological invariants, and argue the possibility of defining new topological invariants in the same manner. Also a non commutative self dual gravity is constructed. Finally a proposal of non commutative quantum cosmology is also given.
Compeán et al. (Sat,) studied this question.