A note on the characteristic rank and related numbers

Abstract

This note quantifies, via a sharp inequality, an interplay between

  1. (a)

    the characteristic rank of a vector bundle over a topological space X

  2. (b)

    the ℤ2-Betti numbers of X, and

  3. (c)

    sums of the numbers of certain partitions of integers.

In a particular context, (c) is transformed into a sum of the readily calculable Betti numbers of the real Grassmann manifolds.

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Correspondence to Ľudovít Balko.

Additional information

Dedicated to Professor Masaharu Morimoto on the occasion of his 60th birthday

Part of this research was carried out while J. Korbaš was a member of the research teams 1/0330/13 and 2/0029/13 supported in part by the grant agency VEGA (Slovakia).

Communicated by Anatolij Dvurečenskij

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Balko, Ľ., Korbaš, J. A note on the characteristic rank and related numbers. Math. Slovaca 64, 1541–1544 (2014). https://doi.org/10.2478/s12175-014-0290-y

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2010 Mathematics Subject Classification

  • Primary 57R20
  • Secondary 05A17

Keywords

  • Stiefel-Whitney class
  • characteristic rank
  • Betti number
  • partitions of integers
  • Grassmann manifold