Loops in generalized Reeb graphs associated to stable circle-valued functions

Batista, Erica Boizan; Costa, João Carlos Ferreira; Nuño–Ballesteros, J. J.

doi:10.5427/jsing.2020.22g

Cited by 2 publications

(1 citation statement)

References 3 publications

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“…The non-singular extensions of Morse functions on closed orientable surfaces were studied by Curley in [5]. Moreover, Curley considered the non-singular extension of a Morse function on S 2 and when the given map can be extended to a submersion on D 3 .…”

Section: Introductionmentioning

confidence: 99%

Non-Singular Extensions of Morse Functions on Disconnected Surfaces

Iwamoto¹

2021

Kyushu J. Math.

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In this paper, we study non-singular extensions of Morse functions on closed orientable surfaces. By a non-singular extension of such a Morse function, we mean an extension to a function without critical points on some compact orientable 3-manifold having as boundary the given surface. In 1977, Curley characterized the existence of non-singular extensions of non-singular boundary germs in terms of combinatorics on associated labeled Reeb graphs. We apply Curley's result to show that every Morse function on a closed orientable (possibly disconnected) surface has a non-singular extension to a 3-manifold that is connected.

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Section: Introductionmentioning

confidence: 99%

Non-Singular Extensions of Morse Functions on Disconnected Surfaces

Iwamoto¹

2021

Kyushu J. Math.

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Realization of a Graph as the Reeb Graph of a Morse–Bott or a Round Function

Gelbukh

2022

SScMath

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We prove criteria for a graph to be the Reeb graph of a function of a given class on a closed manifold: Morse–Bott, round, and in general smooth functions whose critical set consists of a finite number of submanifolds. The criteria are given in terms of whether the graph admits an orientation, which we call S-good orientation, with certain conditions on the degree of sources and sinks, similar to the known notion of good orientation in the context of Morse functions. We also study when such a function is the height function associated with an immersion of the manifold. The condition for a graph to admit an S-good orientation can be expressed in terms of the leaf blocks of the graph.

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Loops in generalized Reeb graphs associated to stable circle-valued functions

Cited by 2 publications

References 3 publications

Non-Singular Extensions of Morse Functions on Disconnected Surfaces

Non-Singular Extensions of Morse Functions on Disconnected Surfaces

Realization of a Graph as the Reeb Graph of a Morse–Bott or a Round Function

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