Elsevier

Topology and its Applications

Volume 230, 1 October 2017, Pages 114-121
Topology and its Applications

Characteristic rank of canonical vector bundles over oriented Grassmann manifolds G˜3,n

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Abstract

We determine the characteristic rank of the canonical oriented vector bundle over G˜3,n for all n3, and as a consequence, we obtain the affirmative answer to a conjecture of Korbaš and Rusin. As an application of this result, we calculate the Z2-cup-length for a new infinite family of manifolds G˜3,n. This result confirms the corresponding claim of Fukaya's conjecture.

MSC

57R20
55R25

Keywords

Stiefel–Whitney class
Characteristic rank
Grassmann manifold
Cup-length

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