Geodesic
Global Topological Invariants of Stable Maps from 3-Manifolds to~$\mathbb R^3$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 214-225.

Voir la notice de l'article provenant de la source Math-Net.Ru

With any stable map from a 3-manifold to $\mathbb R^3$, we associate a graph with weights in its vertices and edges. These graphs are $\mathcal A$-invariants from a global viewpoint. We study their properties and show that any tree with zero weights in its vertices and aleatory weights in its edges can be the graph of a stable map from $S^3$ to $\mathbb R^3$. 
@article{TM_2009_267_a16,
     author = {C. Mendes de Jesus and R. Oset Sinha and M. C. Romero Fuster},
     title = {Global {Topological} {Invariants} of {Stable} {Maps} from {3-Manifolds} to~$\mathbb R^3$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {214--225},
     publisher = {mathdoc},
     volume = {267},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2009_267_a16/}
}
TY  - JOUR
AU  - C. Mendes de Jesus
AU  - R. Oset Sinha
AU  - M. C. Romero Fuster
TI  - Global Topological Invariants of Stable Maps from 3-Manifolds to~$\mathbb R^3$
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2009
SP  - 214
EP  - 225
VL  - 267
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2009_267_a16/
LA  - en
ID  - TM_2009_267_a16
ER  - 
%0 Journal Article
%A C. Mendes de Jesus
%A R. Oset Sinha
%A M. C. Romero Fuster
%T Global Topological Invariants of Stable Maps from 3-Manifolds to~$\mathbb R^3$
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2009
%P 214-225
%V 267
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2009_267_a16/
%G en
%F TM_2009_267_a16
C. Mendes de Jesus; R. Oset Sinha; M. C. Romero Fuster. Global Topological Invariants of Stable Maps from 3-Manifolds to~$\mathbb R^3$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 214-225. http://geodesic.mathdoc.fr/item/TM_2009_267_a16/

[1] Arnold V. I., “Smooth functions statistics”, Funct. Anal. and Other Math., 1:2 (2006), 125–133 | MR

[2] Arnold V. I., “Statistika i klassifikatsiya topologii periodicheskikh funktsii i trigonometricheskikh mnogochlenov”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12, no. 1, 2006, 15–24 | MR | Zbl

[3] Arnold V. I., “Topological classification of Morse functions and generalisations of Hilbert's 16th problem”, Math. Phys. Anal. and Geom., 10 (2007), 227–236 | DOI | MR | Zbl

[4] de Rezende K. A., Franzosa R. D., “Lyapunov graphs and flows on surfaces”, Trans. Amer. Math. Soc., 340:2 (1993), 767–784 | DOI | MR | Zbl

[5] Franks J., “Nonsingular Smale flows on $S^3$”, Topology, 24 (1985), 265–282 | DOI | MR | Zbl

[6] Golubitsky M., Guillemin V., Stable mappings and their singularities, Grad. Texts Math., 14, Springer, New York, 1973 | DOI | MR | Zbl

[7] Hacon D., Mendes de Jesus C., Romero Fuster M. C., “Fold maps from the sphere to the plane”, Exp. Math., 15:4 (2006), 491–497 | DOI | MR | Zbl

[8] Hacon D., Mendes de Jesus C., Romero Fuster M. C., “Stable maps from surfaces to the plane with prescribed branching data”, Topol. and Appl., 154:1 (2007), 166–175 | DOI | MR | Zbl

[9] Hacon D., Mendes de Jesus C., Romero Fuster M. C., “Topological invariants of stable maps from a surface to the plane from a global viewpoint”, Real and complex singularities, Lect. Notes Pure and Appl. Math., 232, M. Dekker, New York, 2003, 227–235 | MR | Zbl

[10] Nicolaescu L. I., “Morse functions statistics”, Funct. Anal. and Other Math., 1:1 (2006), 97–103 | MR

[11] Nikolaev I., “Graphs and flows on surfaces”, Ergodic Theory and Dyn. Syst., 18:1 (1998), 207–220 | DOI | MR | Zbl

[12] Oset Sinha R., Romero Fuster M. C., First order semi-local invariants for stable maps from 3-manifolds to $\mathbb R^3$, Preprint, Univ. València, 2007 | MR

[13] Peixoto M. M., “On the classification of flows on 2-manifolds”, Dynamical systems, Proc. Symp. (Univ. Bahia, Salvador, 1971), Acad. Press, New York, 1973, 389–419 | MR

[14] Vassiliev V., Complements of discriminants of smooth maps: topology and applications, Amer. Math. Soc., Providence, RI, 1992 | MR