### Realization of a graph as the Reeb graph of a Morse function on a manifold

DOI: http://dx.doi.org/10.12775/TMNA.2018.029

#### Abstract

#### Keywords

#### References

S. Biasotti, D. Giorgi, M. Spagnuolo and B. Falcidieno, Reeb graphs for shape analysis and applications, Theoret. Comput. Sci. 392 (2008), 5–22.

K. Cole-McLaughlin, H. Edelsbrunner, J. Harer, V. Natarajan and V. Pascucci, Loops in Reeb graphs of 2-manifolds, Discrete Comput. Geom. 32 (2004), 231–244.

I. Gelbukh, Loops in Reeb graphs of n-manifolds, Discrete Comput. Geom. 59 (2018), no. 4, 843–863.

I. Gelbukh, The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations, Math. Slovaca 67 (2017), 645–656.

M. Kaluba, W. Marzantowicz and N. Silva, On representation of the Reeb graph as a sub-complex of manifold, Topol. Methods Nonlinear Anal. 45 (2015), no. 1, 287–307.

M.A. Kervaire and J.W. Milnor, Groups of Homotopy Spheres I, Ann. of Math. (2), vol. 77, no. 3. (May, 1963), 504–537.

J. Martinez-Alfaro, I.S. Meza-Sarmiento and R. Oliveira, Topological classification of simple Morse Bott functions on surfaces, Contemp. Math. 675 (2016), 165–179.

Y. Masumoto and O. Saeki , A smooth function on a manifold with given Reeb graph, Kyushu J. Math. 65 (2011), no. 1, 75–84.

J.W. Milnor, Differential Topology, Lectures on Modern Mathematics, Vol. II, Wiley, New York, 1964, 165–183.

J.W. Milnor, Lectures on the h-Cobordism Theorem, Princeton University Press, Princeton, 1965.

G. Reeb, Sur les points singuliers d’une forme de Pfaff complètement intégrable ou d’une fonction numérique, C.R. Acad. Sci. Paris 222 (1946), 847–849.

V.V. Sharko, About Kronrod–Reeb graph of a function on a manifold, Methods Funct. Anal. Topology 12 (2006), 389–396.

F. Takens, The minimal number of critical points of a function on a compact manifold and the Lusternik–Schnirelman category, Invent. Math. 6 (1968), 197–244.

### Refbacks

- There are currently no refbacks.