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Even- vs. Odd-dimensional Charney–Davis Conjecture

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More than once we have heard that the Charney–Davis Conjecture makes sense only for odd-dimensional spheres. This is to point out that in fact it is also a statement about even-dimensional spheres.


  1. 1.

    Charney, R., Davis, M.: The Euler characteristic of a non-positively curved, piecewise Euclidean manifold. Pac. J. Math. 171, 117–137 (1995)

  2. 2.

    Davis, M.W.: The Geometry and Topology of Coxeter Groups. London Mathematical Society Monographs Series, vol. 32. Princeton University Press, Princeton (2008)

  3. 3.

    Gal, Ś.R.: Real Root Conjecture fails for five and higher dimensional spheres. Discrete Comput. Geom. 34, 269–284 (2005)

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Correspondence to Światosław R. Gal.

Additional information

The research of first author was partially supported by Polish N201 012 32/0718 grant.

The research of second author was partially supported by the NSF grant DMS-0706259.

T. Januszkiewicz is on leave from Mathematical Institute, Wrocław University.

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Gal, Ś.R., Januszkiewicz, T. Even- vs. Odd-dimensional Charney–Davis Conjecture. Discrete Comput Geom 44, 802–804 (2010). https://doi.org/10.1007/s00454-009-9210-2

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  • Flag complex
  • h-vector
  • Charney–Davis conjecture

Mathematics Subject Classification (2000)

  • 52B70
  • 52B11
  • 06A07