Geodesic
Almost periodic flows on 3–manifolds
Delp, Kelly1
1Mathematics Department, California Polytechnic State University, San Luis Obispo CA 93407, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 157-180
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

A 3–manifold which supports a periodic flow is a Seifert fibered space. We define a notion of almost periodic flow and give conditions under which a manifold supporting an almost periodic flow is Seifert fibered. It is well-known that ℝ3 does not support fixed point free periodic flows, and our results include that ℝ3 does not support certain almost periodic flows.

DOI : 10.2140/agt.2007.7.157
Keywords: 3–manifold, almost periodic flow, Seifert fibered space

Delp, Kelly  1

1 Mathematics Department, California Polytechnic State University, San Luis Obispo CA 93407, USA 
@article{10_2140_agt_2007_7_157,
     author = {Delp, Kelly},
     title = {Almost periodic flows on 3{\textendash}manifolds},
     journal = {Algebraic and Geometric Topology},
     pages = {157--180},
     year = {2007},
     volume = {7},
     number = {1},
     doi = {10.2140/agt.2007.7.157},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.157/}
}
TY  - JOUR
AU  - Delp, Kelly
TI  - Almost periodic flows on 3–manifolds
JO  - Algebraic and Geometric Topology
PY  - 2007
SP  - 157
EP  - 180
VL  - 7
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.157/
DO  - 10.2140/agt.2007.7.157
ID  - 10_2140_agt_2007_7_157
ER  - 
%0 Journal Article
%A Delp, Kelly
%T Almost periodic flows on 3–manifolds
%J Algebraic and Geometric Topology
%D 2007
%P 157-180
%V 7
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.157/
%R 10.2140/agt.2007.7.157
%F 10_2140_agt_2007_7_157
Delp, Kelly. Almost periodic flows on 3–manifolds. Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 157-180. doi: 10.2140/agt.2007.7.157

[1] M L Cartwright, Almost periodic flows and solutions of differential equations, Math. Nachr. 32 (1966) 257

[2] A Casson, D Jungreis, Convergence groups and Seifert fibered 3–manifolds, Invent. Math. 118 (1994) 441

[3] M P Do Carmo, Riemannian geometry, Mathematics: Theory Applications, Birkhäuser (1992)

[4] D Gabai, Convergence groups are Fuchsian groups, Ann. of Math. $(2)$ 136 (1992) 447

[5] G Mess, The Seifert conjecture and groups which are quasiisometric to planes, preprint

[6] P Petersen, Riemannian geometry, Graduate Texts in Mathematics 171, Springer (1998)

[7] P Scott, The geometries of 3–manifolds, Bull. London Math. Soc. 15 (1983) 401

[8] P Scott, There are no fake Seifert fibre spaces with infinite $\pi_1$, Ann. of Math. $(2)$ 117 (1983) 35

[9] P A Smith, A theorem on fixed points for periodic transformations, Ann. of Math. $(2)$ 35 (1934) 572

[10] P Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988) 1

[11] F Waldhausen, Gruppen mit Zentrum und 3–dimensionale Mannigfaltigkeiten, Topology 6 (1967) 505

Cité par Sources :