A note on the characteristic rank of null-cobordant manifolds

Abstract

We give an upper bound for the characteristic rank of smooth closed null-cobordant manifolds and apply it to the Grassmann manifolds of oriented vector subspaces in Euclidean space. The bound turns out to be sharp: it coincides with the exact value of characteristic rank for the Grassmann manifolds of oriented 2-dimensional vector subspaces in odd-dimensional Euclidean space.

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Correspondence to Július Korbaš.

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Balko, L., Korbaš, J. A note on the characteristic rank of null-cobordant manifolds. Acta Math Hung 140, 145–150 (2013). https://doi.org/10.1007/s10474-012-0279-3

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Key words and phrases

  • null-cobordant (cobordant to zero) manifold
  • Stiefel–Whitney characteristic class
  • characteristic rank
  • oriented Grassmann manifold

Mathematics Subject Classification

  • 57R20
  • 55R10
  • 57R19
  • 57R22