Geodesic
Some Algebraic Properties of Cerf Diagrams of One-Parameter Function Families
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 1-13

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We obtain results concerning Arnold's problem about a generalization of the Pontryagin–Thom construction in cobordism theory to real algebraic functions. The Pontryagin–Thom construction in the Wells form is transferred to the space of real functions. The relation of the problem with algebraic $K$-theory and the $h$-principle due to Eliashberg and Mishachev is revealed.
Keywords: wrinkle, Pontryagin–Thom construction, $h$-principle. 
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     title = {Some {Algebraic} {Properties} of {Cerf} {Diagrams} of {One-Parameter} {Function} {Families}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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P. M. Akhmet'ev; D. Repovš; M. Cencelj. Some Algebraic Properties of Cerf Diagrams of One-Parameter Function Families. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 1-13. http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a0/