Are there any good references for Cerf theory, written in English? The main references I see are usually Cerf's own papers in French. In particular, I am looking for a source developing the fundamental result that any 1-parameter family of functions between two Morse functions can be approximated by a family which is Morse at all but finitely many degenerate times, along with the classification (seen on wikipedia for example) of these degenerate points.
2026-03-27 02:33:07.1774578787
Recommendations for Cerf theory?
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I believe A. E. Hatcher and J. B. Wagoner, Pseudo-isotopies of compact manifold, Astérisque, vol. 6. (1973) is self-contained and goes beyond what Cerf proved in J. Cerf, La stratification naturelle de functions différentiables réelles et le théorème de la pseudo-isotopie, Publ. Math., Inst. Hautes Etud. Sci., vol. 39 (1970), pp. 5-173.