Comptes Rendus
no. 8
Topology/Geometry
Cut loci in lens manifolds
[Cut loci dans les espaces lenticulaires]

Présenté par : Étienne Ghys

Sergei Anisov1
1 Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands
Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 595-600.

Les cut loci dans les variétés géométriques de dimension 3 par rapport à leurs métriques naturelles forment une classe remarquable d'épines. Par exemple, ces épines ont un petit nombre de sommets. En appliquant cette idée aux espaces lenticulaires, nous étudions des rapports entre leurs géométrie et topologie, les types combinatoires des enveloppes convexes des Zp-orbites, et des estimations de distance de rotation entre triangulations spécifiques d'un p-gone.

Cut loci in geometric three-manifolds equipped with their natural metrics are an interesting source of spines with small number of vertices. An application of this principle to lens manifolds reveals an interplay between their geometry and topology, combinatorial types of convex hulls of group orbits, and estimates of rotation distance between certain triangulations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.01.025
Sergei Anisov 1

1 Department of Mathematics, Utrecht University, P.O. Box 80.010, NL-3508 TA Utrecht, The Netherlands 
@article{CRMATH_2006__342_8_595_0,
     author = {Sergei Anisov},
     title = {Cut loci in lens manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {595--600},
     publisher = {Elsevier},
     volume = {342},
     number = {8},
     year = {2006},
     doi = {10.1016/j.crma.2006.01.025},
     language = {en},
}
TY  - JOUR
AU  - Sergei Anisov
TI  - Cut loci in lens manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 595
EP  - 600
VL  - 342
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2006.01.025
LA  - en
ID  - CRMATH_2006__342_8_595_0
ER  - 
%0 Journal Article
%A Sergei Anisov
%T Cut loci in lens manifolds
%J Comptes Rendus. Mathématique
%D 2006
%P 595-600
%V 342
%N 8
%I Elsevier
%R 10.1016/j.crma.2006.01.025
%G en
%F CRMATH_2006__342_8_595_0
Sergei Anisov. Cut loci in lens manifolds. Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 595-600. doi : 10.1016/j.crma.2006.01.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.01.025/

[1] S. Anisov Geometrical spines of lens manifolds | arXiv

[2] M. Berger A Panoramic View of Riemannian Geometry, Springer-Verlag, Berlin, 2003

[3] M. Buchner The structure of the cut locus in dimension less than or equal to six, Compositio Math., Volume 37 (1978), pp. 103-119

[4] B. Casler An embedding theorem for connected 3-manifolds with boundary, Proc. Amer. Math. Soc., Volume 16 (1965), pp. 559-566

[5] Sh. Kobayasi; K. Nomizu Foundations of Differential Geometry, vol. II, John Wiley & Sons, Inc., New York, 1969

[6] S. Matveev Complexity theory of three-dimensional manifolds, Acta Appl. Math., Volume 19 (1990), pp. 101-130

[7] S. Matveev Algorithmic Topology and Classification of 3-Manifolds, Springer-Verlag, Berlin, 2003

[8] Polymake: A tool for the algorithmic treatment of polytopes and polyhedra, www.math.tu-berlin.de/polymake

[9] F. Preparata; M. Shamos Computational Geometry. An Introduction, Springer-Verlag, New York, 1985

[10] D. Sleator; R. Tarjan; W. Thurston Rotation distance, triangulations, and hyperbolic geometry, J. Amer. Math. Soc., Volume 1 (1988) no. 3, pp. 647-681

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

A new cichlid fish in the Sahara: The Ounianga Serir lakes (Chad), a biodiversity hotspot in the desert

Sébastien Trape

C. R. Biol (2016)

On the difficulty of finding spines

Cyril Lacoste

C. R. Math (2018)

A new species of Discocyrtanus from Mato Grosso, Brazil (Opiliones: Gonyleptidae) with a key to the species of the genus

Rafael N. Carvalho; Adriano B. Kury

C. R. Biol (2017)