Geodesic
Non-singular graph-manifolds of dimension 4
Mozgova, A1
1Laboratoire d’analyse non linéaire et géométrie, Université d’Avignon, 33, rue Louis Pasteur, 84000 Avignon, France, Laboratoire Emile Picard, UMP 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse, France
Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 1051-1073
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

A compact 4–dimensional manifold is a non-singular graph-manifold if it can be obtained by the glueing T2–bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the bundle structures, the graph-structure is called reduced. We prove that any homotopy equivalence of closed oriented 4–manifolds with reduced nonsingular graph-structures is homotopic to a diffeomorphism preserving the structures.

DOI : 10.2140/agt.2005.5.1051
Keywords: graph-manifold, $\pi_1$–injective submanifold

Mozgova, A  1

1 Laboratoire d’analyse non linéaire et géométrie, Université d’Avignon, 33, rue Louis Pasteur, 84000 Avignon, France, Laboratoire Emile Picard, UMP 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse, France 
@article{10_2140_agt_2005_5_1051,
     author = {Mozgova, A},
     title = {Non-singular graph-manifolds of dimension 4},
     journal = {Algebraic and Geometric Topology},
     pages = {1051--1073},
     year = {2005},
     volume = {5},
     number = {3},
     doi = {10.2140/agt.2005.5.1051},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1051/}
}
TY  - JOUR
AU  - Mozgova, A
TI  - Non-singular graph-manifolds of dimension 4
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 1051
EP  - 1073
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1051/
DO  - 10.2140/agt.2005.5.1051
ID  - 10_2140_agt_2005_5_1051
ER  - 
%0 Journal Article
%A Mozgova, A
%T Non-singular graph-manifolds of dimension 4
%J Algebraic and Geometric Topology
%D 2005
%P 1051-1073
%V 5
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.1051/
%R 10.2140/agt.2005.5.1051
%F 10_2140_agt_2005_5_1051
Mozgova, A. Non-singular graph-manifolds of dimension 4. Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 1051-1073. doi: 10.2140/agt.2005.5.1051

[1] R Abraham, J Robbin, Transversal mappings and flows, An appendix by Al Kelley, W. A. Benjamin, New York-Amsterdam (1967)

[2] M Culler, Using surfaces to solve equations in free groups, Topology 20 (1981) 133

[3] D Eisenbud, W Neumann, Three-dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies 110, Princeton University Press (1985)

[4] A T Fomenko, K Tsishang, A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom, Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990) 546

[5] C J Earle, J Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969) 19

[6] J A Hillman, The algebraic characterization of geometric 4–manifolds, London Mathematical Society Lecture Note Series 198, Cambridge University Press (1994)

[7] J A Hillman, Four-manifolds, geometries and knots, Geometry Topology Monographs 5, Geometry Topology Publications, Coventry (2002)

[8] M W Hirsch, Immersions of manifolds, Trans. Amer. Math. Soc. 93 (1959) 242

[9] R C Lyndon, M P Schützenberger, The equation $a^{M}=b^{N}c^{P}$ in a free group, Michigan Math. J. 9 (1962) 289

[10] W Magnus, A Karrass, D Solitar, Combinatorial group theory, Dover Publications (1976)

[11] W Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973) 239

[12] J R Munkres, Elementary differential topology, Lectures given at Massachusetts Institute of Technology, Fall 1961, Princeton University Press (1966)

[13] X Rong, The limiting eta invariants of collapsed three-manifolds, J. Differential Geom. 37 (1993) 535

[14] P Scott, T Wall, Topological methods in group theory, from: "Homological group theory (Proc. Sympos., Durham, 1977)", London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137

[15] H Seifert, W Threlfall, Seifert and Threlfall: a textbook of topology, Pure and Applied Mathematics 89, Academic Press (1980)

[16] S Smale, The classification of immersions of spheres in Euclidean spaces, Ann. of Math. $(2)$ 69 (1959) 327

[17] J Stallings, Group theory and three-dimensional manifolds, Yale University Press (1971)

[18] F Waldhausen, Eine Klasse von 3–dimensionalen Mannigfaltigkeiten. I, II, Invent. Math. 3 $(1967)$, 308–333; ibid. 4 (1967) 87

[19] F Waldhausen, On irreducible 3–manifolds which are sufficiently large, Ann. of Math. $(2)$ 87 (1968) 56

Cité par Sources :