This note quantifies, via a sharp inequality, an interplay between
the characteristic rank of a vector bundle over a topological space X
the ℤ2-Betti numbers of X, and
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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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
2010 Mathematics Subject Classification
- Primary 57R20
- Secondary 05A17
- Stiefel-Whitney class
- characteristic rank
- Betti number
- partitions of integers
- Grassmann manifold