A smooth function on a manifold with given reeb graph

Yasutaka Masumoto, Osamu Saeki

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We show that any finite graph without loops can be realized as the Reeb graph of a smooth function on a closed manifold with finitely many critical values, but possibly with positive dimensional critical point set. We also show that such a function can be chosen as the height function on a surface immersed in 3-space, provided that the graph has no isolated vertices.

Original languageEnglish
Pages (from-to)75-84
Number of pages10
JournalKyushu Journal of Mathematics
Volume65
Issue number1
DOIs
Publication statusPublished - Jun 10 2011

Fingerprint

Reeb Graph
Smooth function
Critical Set
Finite Graph
Point Sets
Critical value
Critical point
Closed
Graph in graph theory

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

A smooth function on a manifold with given reeb graph. / Masumoto, Yasutaka; Saeki, Osamu.

In: Kyushu Journal of Mathematics, Vol. 65, No. 1, 10.06.2011, p. 75-84.

Research output: Contribution to journalArticle

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