Morse functions with sphere fibers

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概要

• 論文の詳細を見る

• A smooth closed manifold is said to be an almost sphere if it admits a Morse function with exactly two critical points. In this paper, we characterize those smooth closed manifolds which admit Morse functions such that each regular fiber is a finite disjoint union of almost spheres. We will see that such manifolds coincide with those which admit Morse functions with at most three critical values. As an application, we give a new proof of the characterization theorem of those closed manifolds which admit special generic maps into the plane. We also discuss homotopy and diffeomorphism invariants of manifolds related to the minimum number of critical values of Morse functions; in particular, the Lusternik-Schnirelmann category and spherical cone length. Those closed orientable $3$-manifolds which admit Morse functions with regular fibers consisting of spheres and tori are also studied.

• 広島大学の論文

著者

• Saeki Osamu

  Faculty Of Mathematics Kyushu University

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• 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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