The strange nongenericness of codimension 1 differential systems in dimension 4 revisited

• Autorzy: Mormul P.
• Języki publikacji: EN

Abstrakty

EN

Strange non-typical behaviour of 3-generated modules of vector fields on 4-dimensional manifolds, at certain generic points of degeneration, has been announced in [5]. A new short proof of that geometric anomaly is now proposed ; it hinges on a careful examination of the Pfaffian equation associated to the respective codimension 1 differential system.

Słowa kluczowe

EN

differential system; module of vector fields; singularity strata; typical nongenericness

PL

analiza matematyczna; analiza na rozmaitościach; moduł pola wektorowego; układ różniczkowy

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2000
• Tom: Vol. 48, no 1
• Strony: 97--102
• Opis fizyczny: Bibliogr. 8 poz.,

Twórcy

autor

Mormul P.

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] B. Jakubczyk, F. Przytycki, Singularities of k-tuples of vector fields, Dissertationes Math., 213 (1984).
• [2] B. Jakubczyk, M. Zhitomirskii, Odd-dimensional Pfaffian equations; reduction to the hypersurface of singular points, C. R. Acad. Sci. Paris Ser. I Math., 325 (1997) 423-428.
• [3] J. Martinet, Sur les singularites des formes differentielles, Ann. Inst. Fourier, 20 (1970) 95-178.
• [4] J. N. Mather, Stability of C' mappings, III: finitely determined map germs, Publ. Math. I.H.E.S., 35 (1968) 127-156.
• [5] P. Mormul, Singularities of triples of vector fields on R4; Bull. Pol. Ac.: Math., 31 (1983) 41-49.
• [6] P. Mormul, Singularities of triples of vector fields on R4: the focusing stratum; Studia Math., 91 (1988) 241-273.
• [7] P. Mormul, M. Zhitomirskii, The structure of the set of singular points of a codimension 1 differential system on a 5-manifold, Trans. Amer. Math. Soc., 342 (1994) 619-629.
• [8] P. Mormul, M. Zhitomirskii, Modules of vector fields, differential forms, and degenerations of differential systems, Israel J. Math., 95 (1996) 411-428.