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

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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/}
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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/