Comptes Rendus
no. 8
Topologie
Intersection norms and one-faced collections
Abdoul Karim Sane1
1 Unité de Mathématiques Pures et Appliquées (UMPA), ENS-Lyon, France
Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 941-956.

Intersection norms are integer norms on the first homology group of a surface. In this article, we give examples of polytopes which are not the dual unit balls of intersection norms, answering a question asked in [2]. On the way, we investigate the set of collections of curves on Σ 2 whose complement is a disk.

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DOI : 10.5802/crmath.118
Abdoul Karim Sane 1

1 Unité de Mathématiques Pures et Appliquées (UMPA), ENS-Lyon, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Abdoul Karim Sane. Intersection norms and one-faced collections. Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 941-956. doi : 10.5802/crmath.118. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.118/

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[2] Marcos Cossarini; Pierre Dehornoy Intersection norms on surfaces and Birkhoff sections for geodesic flows (2016) (https://arxiv.org/abs/1604.06688)

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[6] Abdoul Karim Sane On dual unit balls of Thurston norms (2020) (https://arxiv.org/abs/2004.04407)

[7] William P. Thurston A norm for the homology of 3-manifolds, Two papers: Genera of the arborescent links and A norm for the homology of 3-manifolds (Memoirs of the American Mathematical Society), Volume 339, American Mathematical Society, 1986, pp. 99-130 | Zbl

[8] Vladimir Turaev A norm for the cohomology of 2-complexes, Algebr. Geom. Topol., Volume 2 (2002), pp. 137-155 | DOI | MR | Zbl

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