Topological complexity of oriented Grassmann manifolds

We study the Z₂-zero-divisor cup-length, denoted by zclZ₂( Gn,3), of the Grassmann manifolds Gn,3 of oriented $3$-dimensional vector subspaces in Rⁿ. Some lower and upper bounds for this invariant are obtained for all integers n≥6. For infinitely many of them the exact value of zclZ₂( Gn,3) is computed, and in the rest of the cases these bounds differ by 1. We thus establish lower bounds for the topological complexity of Grassmannians Gn,3.