Cobordism of Morse maps and its application to map germs

Kazuichi Ikegami, Osamu Saeki

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Let f: M S1 be a Morse map of a closed manifold M into the circle, where a Morse map is a smooth map with only nondegenerate critical points. In this paper, we classify such maps up to fold cobordism. In the course of the classification, we get several fold cobordism invariants for such Morse maps. We also consider a slightly general situation where the source manifold M has boundary and the map f restricted to the boundary has no critical points. Let g: (Rm, 0) (R2, 0), m ≥ 2, be a generic smooth map germ, where the target R2 is oriented. Using the above-mentioned fold cobordism invariants, we show that the number of cusps with a prescribed index appearing in a C stable perturbation of g, counted with signs, gives a topological invariant of g.

Original languageEnglish
Pages (from-to)235-254
Number of pages20
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
Publication statusPublished - Jul 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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