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A Subexponential Size Triangulation of ℝPn

Abstract

We break the exponential barrier for triangulations of the real projective space, constructing a trianglation of ℝPn with \({e^{\left({{1 \over 2} + o(1)} \right)\sqrt n \log n}}\) vertices.

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Acknowledgments

We wish to thank Wolfgang Kühnel and Alexis Marin for very extensive and helpful remarks on the first version of the paper and anonymous referees for their comments and their suggestion of how to simplify the last part of the proof of Claim 3.3. We also wish to thank Arseniy Akopyan, Xavier Goaoc, Andrey Kupavskii, Gaku Liu, János Pach and Dömötör Pálvölgyi for helpful discussions.

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Correspondence to Karim Adiprasito.

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Dedicated to Wolfgang Kühnel on the occasion of his 70th birthday.

Has received funding from the European Research Council under the European Unions Seventh Framework Programme ERC Grant agreement ERC StG 716424 — CASe and the Israel Science Founda-tion under ISF Grant 1050/16.

Has received funding from the European Research Council under the European Unions Seventh Framework Programme ERC Grant agreement ERC StG 716424 — CASe.

Supported by the Federal professorship program grant 1.456.2016/1.4 and the Russian Foundation for Basic Research grants 18-01-00036 and 19-01-00169.

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Adiprasito, K., Avvakumov, S. & Karasev, R. A Subexponential Size Triangulation of ℝPn. Combinatorica 42, 1–8 (2022). https://doi.org/10.1007/s00493-021-4602-x

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  • DOI: https://doi.org/10.1007/s00493-021-4602-x

Mathematics Subject Classification (2010)

  • 57Q15