A SMOOTH FUNCTION ON A MANIFOLD WITH GIVEN REEB GRAPH

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概要

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• 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.

著者

• Saeki Osamu

  Faculty Of Mathematics Kyushu University

• Masumoto Yasutaka

  Shiroishi High School

関連論文

• ELIMINATION OF DEFINITE FOLD
• Generic smooth maps with sphere fibers : Dedicated to Professor Yukio Matsumoto on the occasion of his 60th birthday
• Morse functions with sphere fibers
• A SMOOTH FUNCTION ON A MANIFOLD WITH GIVEN REEB GRAPH
• Cobordism group of Morse functions on surfaces : Dedicated to Professor Tatsuo Suwa on his sixtieth birthday
• Height functions on surfaces with three critical values

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