Archiv der Mathematik

, Volume 89, Issue 6, pp 570–576 | Cite as

On the genus of real projective spaces



We construct a crystallization of the real projective space \({\mathbb{R}}P^n\) whose associated contracted complex is minimal with respect to the number of n-simplexes. Then we compute the regular genus of \({\mathbb{R}}P^n\), which is the minimum genus of a closed connected surface into which a crystallization of \({\mathbb{R}}P^n\) regularly embeds.

Mathematics Subject Classification (2000).

57N15 57Q15 05C10 


Colored graph crystallization contracted triangulation 2–cell embedding regular genus suspension 


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Copyright information

©  2007

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Modena e Reggio EmiliaModenaItaly

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