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DOI:

https://doi.org/10.12775/TMNA.2021.044

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Bibliografia

R. Bott, Nondegenerate critical manifolds, Ann. of Math. 60 (1954), 248–261.

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

I. Gelbukh, Approximation of metricsSpaces by Reeb graphs: cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannia manifolds, Filomat, arxiv:1903.00777. (in press)

M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities, Graduate Texts in Mathematics, vol. 14, Springer–Verlag, 1974.

N. Kitazawa, Smooth maps compatible with simplicial structures and preimages, arxiv: 1802.06381v6.

N. Kitazawa, Structures of cobordism-like modules induced from generic maps of codimension −2, arxiv:1901.04994v1.

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), 75–84.

L.P. Michalak, Realization of a graph as the Reeb graph of a Morse function on a manifold, Topol. Methods Nonlinear Anal. 52 (2018), no. 2, 749–762.

L.P. Michalak, Combinatorial modifications of Reeb graphs and the realization problem, Discrete Comput. Geometry 65 (2021), 1038–1060.

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G. Reeb, Sur les points singuliers d´une forme de Pfaff complétement intègrable ou d´une fonction numérique, Comptes Rendus Hebdomadaires des Séances de I´Académie des Sciences 222 (1946), 847–849.

O. Saeki, Notes on the topology of folds, J. Math. Soc. Japan 44 (1992), no. 3, 551–566.

O. Saeki, Topology of singular fibers of differntiable maps, Lecture Notes in Math., vol. 1854, Springer–Verlag, 2004.

O. Saeki, Morse functions with sphere fibers, Hiroshima Math. J. 36 (2006), no. 1, 141–170.

O. Saeki, Reeb spaces of smooth functions on manifolds, Intermational Mathematics Research Notices, maa301, DOI: 10.1093/imrn/maa301, arxiv:2006.01689.

O. Saeki and M. Takase, Desingularizing special generic maps, J. Gökova Geom. Topol. GGT 7 (2013), 1–24.

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

Opublikowane

2022-06-12

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1.
Topological Methods in Nonlinear Analysis [online]. 12 czerwiec 2022, T. 59, nr 2B, s. 897–912. [udostępniono 22.7.2024]. DOI 10.12775/TMNA.2021.044.

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