Abstract We prove that the topological complexity of a quaternionic flag manifold is half of its real dimension. For the real oriented Grassmann manifolds G͠n,k, 3 ≤ k ≤ [n/2], the zero-divisor cup-length of the rational cohomology of G͠n,k is computed in terms of n and k which gives a lower bound for the topological complexity of G͠n,k, TC(G͠n,k). When k = 3, it is observed in certain cases that better lower bounds for TC(G͠n,3) are obtained using ℤ2-cohomology.

中文翻译：

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关于格拉斯曼流形的拓扑复杂度

摘要 我们证明了四元标志流形的拓扑复杂度是其实维数的一半。对于实向 Grassmann 流形 G͠n,k, 3 ≤ k ≤ [n/2]，G͠n,k 的有理上同调的零除数杯长是根据 n 和 k 计算的，这给出了G͠n,k, TC(G͠n,k)的拓扑复杂度。当 k = 3 时，在某些情况下观察到使用 ℤ2-上同调可以获得更好的 TC(G͠n,3) 下界。