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On maximality of the cup-length of flag manifolds

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Abstract

We investigate which real flag manifolds of the form

$$F(1,\ldots,1,2,\ldots,2,m)$$

have the \({\mathbb Z_2}\)-cup-length equal to the dimension. We obtain a complete classification of such manifolds of the form \({F(1,\ldots,1,2,m)}\) and \({F(1,\ldots,1,2,2,m)}\). Additionally, we provide an infinite family of manifolds \({F(1,\ldots,1,2,\ldots,2,m)}\) which give the negative answer to a question from J. Korbaš and J. Lörinc [5].

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References

  1. Berstein I.: On the Lusternik–Schnirelmann category of Grassmannians. Math. Proc. Cambridge Philos. Soc. 79, 129–134 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hiller H.: On the cohomology of real Grassmanians. Trans. Amer. Math. Soc. 257, 512–533 (1980)

    Article  MathSciNet  Google Scholar 

  3. Korbaš J.: Bounds for the cup-length of Poincaré spaces and their applications. Topology Appl. 153, 2976–2986 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Korbaš J.: The cup-length of the oriented Grassmannians vs a new bound for zerocobordant manifolds. Bull. Belg. Math. Soc. Simon Stevin 17, 69–81 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Korbaš J., Lörinc J.: The \({\mathbb{Z}_2}\)-cohomology cup-length of real flag manifolds. Fund. Math. 178, 143–158 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Radovanović, On the \({\mathbb{Z}_2}\)-cohomology cup-length of some real flag manifolds, Filomat, accepted for publication.

  7. Stong R.E.: Cup products in Grassmannians. Topology Appl. 13, 103–113 (1982)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, Belgrade, Serbia

    Z. Z. Petrović, B. I. Prvulović & M. Radovanović

Authors
  1. Z. Z. Petrović
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  2. B. I. Prvulović
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  3. M. Radovanović
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Corresponding author

Correspondence to B. I. Prvulović.

Additional information

The first author was partially supported by Ministry of Education, Science and Technological Development of Republic of Serbia Project #174032.

The second author was partially supported by Ministry of Education, Science and Technological Development of Republic of Serbia Project #174034.

The third author was partially supported by Ministry of Education, Science and Technological Development of Republic of Serbia Project #174008.

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Petrović, Z.Z., Prvulović, B.I. & Radovanović, M. On maximality of the cup-length of flag manifolds. Acta Math. Hungar. 149, 448–461 (2016). https://doi.org/10.1007/s10474-016-0625-y

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  • DOI: https://doi.org/10.1007/s10474-016-0625-y

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