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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
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 
@article{CRMATH_2020__358_8_941_0,
     author = {Abdoul Karim Sane},
     title = {Intersection norms and one-faced collections},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {941--956},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {8},
     year = {2020},
     doi = {10.5802/crmath.118},
     language = {en},
}
TY  - JOUR
AU  - Abdoul Karim Sane
TI  - Intersection norms and one-faced collections
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 941
EP  - 956
VL  - 358
IS  - 8
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.118
LA  - en
ID  - CRMATH_2020__358_8_941_0
ER  - 
%0 Journal Article
%A Abdoul Karim Sane
%T Intersection norms and one-faced collections
%J Comptes Rendus. Mathématique
%D 2020
%P 941-956
%V 358
%N 8
%I Académie des sciences, Paris
%R 10.5802/crmath.118
%G en
%F CRMATH_2020__358_8_941_0
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/

[1] Tarik Aougab; Shinnyih Huang Minimally intersecting filling pairs on surfaces, Algebr. Geom. Topol., Volume 15 (2015) no. 2, pp. 903-932 | DOI | MR | Zbl

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

[3] Albert Fathi; François Laudenbach; Valentin Poénaru Thurston’s work on surfaces, Mathematical Notes, 48, Princeton University Press, 2012 | MR | Zbl

[4] Joel Hass; Peter Scott Shortening curves on surfaces, Topology, Volume 33 (1994) no. 1, pp. 25-43 | DOI | MR | Zbl

[5] Mikael de la Salle On norms taking integer values on the integer lattice, C. R. Math. Acad. Sci. Paris, Volume 354 (2016) no. 6, pp. 611-613 | DOI | MR | Zbl

[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

Cité par Sources :

Commentaires - Politique