Geodesic
Horizontal vector fields and Seifert fiberings
Hammerlindl, Andy1
1School of Mathematics, Monash University, Clayton VIC, Australia
Algebraic and Geometric Topology, Tome 20 (2020) no. 6, pp. 2779-2820
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We give a classification of the topology of vector fields which are nowhere tangent to the fibers of a Seifert fibering.

Classification : 55R05, 57R18, 57R25
Keywords: Seifert fiberings, vector fields, lens spaces

Hammerlindl, Andy  1

1 School of Mathematics, Monash University, Clayton VIC, Australia 
@article{AGT_2020_20_6_a1,
     author = {Hammerlindl, Andy},
     title = {Horizontal vector fields and {Seifert} fiberings},
     journal = {Algebraic and Geometric Topology},
     pages = {2779--2820},
     year = {2020},
     volume = {20},
     number = {6},
     url = {http://geodesic.mathdoc.fr/item/AGT_2020_20_6_a1/}
}
TY  - JOUR
AU  - Hammerlindl, Andy
TI  - Horizontal vector fields and Seifert fiberings
JO  - Algebraic and Geometric Topology
PY  - 2020
SP  - 2779
EP  - 2820
VL  - 20
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/AGT_2020_20_6_a1/
ID  - AGT_2020_20_6_a1
ER  - 
%0 Journal Article
%A Hammerlindl, Andy
%T Horizontal vector fields and Seifert fiberings
%J Algebraic and Geometric Topology
%D 2020
%P 2779-2820
%V 20
%N 6
%U http://geodesic.mathdoc.fr/item/AGT_2020_20_6_a1/
%F AGT_2020_20_6_a1
Hammerlindl, Andy. Horizontal vector fields and Seifert fiberings. Algebraic and Geometric Topology, Tome 20 (2020) no. 6, pp. 2779-2820. http://geodesic.mathdoc.fr/item/AGT_2020_20_6_a1/

[1] T Barbot, Flots d’Anosov sur les variétés graphées au sens de Waldhausen, Ann. Inst. Fourier (Grenoble) 46 (1996) 1451 | DOI

[2] E J Brody, The topological classification of the lens spaces, Ann. of Math. 71 (1960) 163 | DOI

[3] S Choi, Geometric structures on 2–orbifolds : exploration of discrete symmetry, 27, Math. Soc. Japan (2012) | DOI

[4] J H Conway, The orbifold notation for surface groups, from: "Groups, combinatorics and geometry" (editors M Liebeck, J Saxl), Lond. Math. Soc. Lect. Note Ser. 165, Cambridge Univ. Press (1992) 438 | DOI

[5] D Eisenbud, U Hirsch, W Neumann, Transverse foliations of Seifert bundles and self-homeomorphism of the circle, Comment. Math. Helv. 56 (1981) 638 | DOI

[6] É Ghys, Flots d’Anosov sur les 3–variétés fibrées en cercles, Ergodic Theory Dynam. Systems 4 (1984) 67 | DOI

[7] A Hammerlindl, R Potrie, M Shannon, Seifert manifolds admitting partially hyperbolic diffeomorphisms, J. Mod. Dyn. 12 (2018) 193 | DOI

[8] A Hatcher, Algebraic topology, Cambridge Univ. Press (2002)

[9] A Hatcher, Notes on basic 3–manifold topology, book project (2007)

[10] M Jankins, W D Neumann, Lectures on Seifert manifolds, 2, Brandeis Univ. (1983)

[11] R Naimi, Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv. 69 (1994) 155 | DOI

[12] P Orlik, Seifert manifolds, 291, Springer (1972) | DOI

[13] M M Peixoto, Structural stability on two-dimensional manifolds, Topology 1 (1962) 101 | DOI

[14] P Scott, The geometries of 3–manifolds, Bull. Lond. Math. Soc. 15 (1983) 401 | DOI