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Stratifications adapted to finite families of differential 1-forms. (Pfaffian geometry. I.). (English) Zbl 0862.32002
This paper claims to be a systematic survey about Pfaffian geometry, but it is neither systematic, nor new, nor interesting. Its level is undergraduate, which is surprising, because it has been published by an international review.
The bibliography is a strange mixture of old (Whitney) and new, far from being systematic or complete. For instance, the works of J. M. Lion are under-represented, the surveys [the reviewer and J. Stasica, “Ensembles sousanalytiques à la polonaise” (1985)] and E. Bierstone and P. D. Milman, “Semi and subanalytic sets”, Publ. Math., Inst. Hautes Étud. sci. 67, 5-42 (1988; Zbl 0674.32002)] are omitted, as well as the reviewer and K. Wachta, “La sous-analyticité de l’application tangente”, Bull. Acad. Pol. Sci., Sér. Sci. Math. 30, 329-331 (1982; Zbl 0526.32007), all very well known to the Polish author, former student of J. Stasica.
The reviewer spent a lot of time in Dijon when this theory took shape. She founds now the remarks like 1.4 displaced, because it is said nowhere that the remark belongs to R. Moussu (1988).
It is regrettable that the second part of this work is forthcoming, as the centre of studies is still in Dijon and for any mathematician on a reasonable level it is better to read the original, very well written, works of Moussu, Roche, Lion, Rollin, at times Cano.
MSC:
32B20 Semi-analytic sets, subanalytic sets, and generalizations
53C12 Foliations (differential geometric aspects)
34C30 Manifolds of solutions of ODE (MSC2000)
32B25 Triangulation and topological properties of semi-analytic andsubanalytic sets, and related questions
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