Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds

Rusin, Tomáš

doi:10.5817/am2018-5-313

Arch. Math. (Brno)

2018

DOI: 10.5817/am2018-5-313

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Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds

Tomáš Rusin¹

Abstract: We estimate the characteristic rank of the canonical k-plane bundle over the oriented Grassmann manifold G n,k. We then use it to compute uniform upper bounds for the Z 2-cup-length of G n,k for n belonging to certain intervals.

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2020

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On the topological complexity of Grassmann manifolds

Ramani

2020

Mathematica Slovaca

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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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On the topological complexity of Grassmann manifolds

Ramani

2020

Mathematica Slovaca

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Bounds for the characteristic rank and cup-length of oriented Grassmann manifolds

Abstract: We estimate the characteristic rank of the canonical k-plane bundle over the oriented Grassmann manifold G n,k. We then use it to compute uniform upper bounds for the Z 2-cup-length of G n,k for n belonging to certain intervals.

Cited by 1 publication

References 10 publications

On the topological complexity of Grassmann manifolds

On the topological complexity of Grassmann manifolds

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