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A note on the characteristic rank and related numbers

Mathematica Slovaca volume 64, pages 1541–1544 (2014)Cite this article

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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References

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Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering of SUT, Námestie slobody 17, SK-812 31, Bratislava, Slovakia

    Ľudovít Balko

  2. Faculty of Mathematics, Physics, and Informatics, Comenius University, Mlynská dolina, SK-842 48, Bratislava, Slovakia

    Július Korbaš

  3. Mathematical Institute of SAS, Štefánikova 49, SK-841 73, Bratislava, Slovakia

    Július Korbaš

Authors
  1. Ľudovít Balko
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  2. Július Korbaš
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Corresponding author

Correspondence to Ľudovít Balko.

Additional information

Communicated by Anatolij Dvurečenskij

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).

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Cite this article

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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  • DOI: https://doi.org/10.2478/s12175-014-0290-y

2010 Mathematics Subject Classification

  • Primary 57R20
  • Secondary 05A17

Keywords

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