2020
DOI: 10.1515/ms-2017-0425
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On the topological complexity of Grassmann manifolds

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.

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