A smooth function on a manifold with given reeb graph

Yasutaka Masumoto, Osamu Saeki

Research output: Contribution to journalArticlepeer-review

7 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 - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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