Geodesic
Local Properties of the Embedding of a Graph in a Three-Manifold
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 517-528

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a finite graph topologically embedded in the interior of a 3-manifold M. Doyle (4) and Debrunner and Fox (3) have noted that the following local homotopy condition at each point p ∈ G is necessary in order for the embedding of G to be tame: For each sufficiently small open set U containing p, there is an open set V such that p ∈ V ⊂ U and if W is any connected open set such that p ∈ W ⊂ V, then the image under the inclusion homomorphism i*: π1(W — G) → π1(U — G) is a free group on n — 1 generators. 
Jr., D. R. McMillan. Local Properties of the Embedding of a Graph in a Three-Manifold. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 517-528. doi: 10.4153/CJM-1966-051-7
@article{10_4153_CJM_1966_051_7,
     author = {Jr., D. R. McMillan},
     title = {Local {Properties} of the {Embedding} of a {Graph} in a {Three-Manifold}},
     journal = {Canadian journal of mathematics},
     pages = {517--528},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-051-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-051-7/}
}
TY  - JOUR
AU  - Jr., D. R. McMillan
TI  - Local Properties of the Embedding of a Graph in a Three-Manifold
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 517
EP  - 528
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-051-7/
DO  - 10.4153/CJM-1966-051-7
ID  - 10_4153_CJM_1966_051_7
ER  - 
%0 Journal Article
%A Jr., D. R. McMillan
%T Local Properties of the Embedding of a Graph in a Three-Manifold
%J Canadian journal of mathematics
%D 1966
%P 517-528
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-051-7/
%R 10.4153/CJM-1966-051-7
%F 10_4153_CJM_1966_051_7

[1] 1. Bing, R. H., Locally tame sets are tame, Ann. of Math., 59 (1954), 145–158. Google Scholar

[2] 2. Bing, R. H., A surface is tame if its complement is, 1-ULC, Trans. Amer. Math. Soc, 101 (1961), 294–305. Google Scholar

[3] 3. Debrunner, H. and Fox, R. H., A mildly wild imbedding of an n-frame, Duke Math. J., 27 (1960), 425–430. Google Scholar

[4] 4. Doyle, P. H., A wild triod in three-space, Duke Math. J., 26 (1959), 263–267. Google Scholar

[5] 5. Edwards, C. H. Jr., A characterization of tame curves in the 3-sphere, Abstract 573-32, Notices Amer. Math. Soc., 7 (1960), 875. Google Scholar

[6] 6. Fox, R. H., On the imbedding of polyhedra in 3-space, Ann. of Math., 49 (1948), 462–470. Google Scholar

[7] 7. Harrold, O. G. Jr., Euclidean domains with uniformly abelian local fundamental groups, Trans. Amer. Math. Soc, 67 (1949), 120–129. Google Scholar

[8] 8. Harrold, O. G. Jr., Euclidean domains with uniformly abelian local fundamental groups, II, Duke Math. J., 17 (1950), 269–272. Google Scholar

[9] 9. Harrold, O. G. Jr., Griffith, H. C., and Posey, E. E., A characterization of tame curves in 3-space, Trans. Amer. Math. Soc, 79 (1955), 12–35. Google Scholar

[10] 10. Harrold, O. G. Jr., and Moise, E. E., Almost locally polyhedral spheres, Ann. of Math., 57 (1953), 575–578. Google Scholar

[11] 11. Hempel, J. P. and McMillan, D. R. Jr., Locally nice embeddings of manifolds, to appear. Google Scholar

[12] 12. Moise, E. E., Affine structures in 3-manifolds, V, The triangulation theorem and Hauptvermutung, Ann. of Math., 56 (1952), 96–114. Google Scholar

[13] 13. Moise, E. E., Affine structures in 3-manifolds, VIII. Invariance of the knot-types; Local tame imbedding, Ann. of Math., 59 (1954), 159–170. Google Scholar

[14] 14. Papakyriakopoulos, C. D., On solid tori, Proc. London Math. Soc. (3), 7 (1957), 281–299. Google Scholar

[15] 15. Papakyriakopoulos, C. D., On Dehn's lemma and the asphericity of knots, Ann. of Math., 66 (1957), 1–26. Google Scholar

[16] 16. Stallings, J. R., On fibering certain 3-manifolds, University of Georgia Conference on Topology of Manifolds (1961), 95–100. Google Scholar

Cité par Sources :