A New Family of Triangulations of ℝPd

Abstract

We construct a family of PL triangulations of the d-dimensional real projective space ℝPd on \(\Theta \left( {{{\left( {\tfrac{{1 + \sqrt 5 }}{2}} \right)}^{d + 1}}} \right)\) vertices for every \(d \geqslant 1\). This improves a construction due to Kühnel on 2d+1 -1 vertices.

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Acknowledgements

We would like to thank Basudeb Datta, Isabella Novik and Martina Juhnke-Kubitzke for helpful comments. We also would like to express our gratitude to the anonymous referees for providing references for results on minimal triangulated manifolds in other settings, as well as an insightful remark on the properness of group actions on PL manifolds. Their detailed feedback greatly helped us to improve earlier versions of the article.

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Correspondence to Hailun Zheng.

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Venturello, L., Zheng, H. A New Family of Triangulations of ℝPd. Combinatorica 41, 127–146 (2021). https://doi.org/10.1007/s00493-020-4351-2

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Mathematics Subject Classification (2010)

  • 57Q15
  • 57R05