Finite c0-determinacy of real analytic map germs with isolated instability
- Moya-Pérez, J. A.
- Nuño Ballesteros, Juan José
ISSN: 0214-1493
Año de publicación: 2020
Volumen: 64
Número: 2
Páginas: 563-575
Tipo: Artículo
Otras publicaciones en: Publicacions matematiques
Resumen
Let f : (Rn; 0) (Rp; 0) be a real analytic map germ with isolated instability. We prove that if n = 2 and p = 2; 3, then f is finitely C0-determined. This result can be seen as a weaker real counterpart of Mather-Gaffney finite determinacy criterion.
Información de financiación
Work partially supported by MICINN Grant PGC2018-094889-B-I00 and by GVA Grant AICO/2019/024.Financiadores
-
Generalitat Valenciana
Spain
- AICO/2019/024
-
Ministerio de Ciencia e Innovación
Spain
- PGC2018-094889-B-I00
Referencias bibliográficas
- H. Brodersen, G. Ishikawa, and L. C. Wilson, A criterion for finite topo-logical determinacy of map-germs, Proc. London Math. Soc. (3) 74(3) (1997),662-700. DOI: 10.1112/S0024611597000221.
- T. Gaffney, Polar multiplicities and equisingularity of map germs, Topology32(1) (1993), 185-223. DOI: 10.1016/0040-9383(93)90045-W.
- T. C. Kuo, A complete determination of C0-suficiency in Jr(2; 1), Invent. Math.8 (1969), 226-235. DOI: 10.1007/BF01406074.
- S. Lojasiewicz, Ensembles semi-analytiques, Notes, 1965.
- W. L. Marar, J. J. Nuño-Ballesteros, and G. Pe~nafort-Sanchis, Doublepoint curves for corank 2 map germs from C2 to C3, Topology Appl. 159(2)(2012), 526-536. DOI: 10.1016/j.topol.2011.09.028.
- J. Milnor, \Singular Points of Complex Hypersurfaces", Annals of MathematicsStudies 61, Princeton University Press, Princeton, N.J.; University of TokyoPress, Tokyo, 1968.
- D. Mond, Some remarks on the geometry and classification of germs ofmaps from surfaces to 3-space, Topology 26(3) (1987), 361-383. DOI: 10.1016/0040-9383(87)90007-3.
- J. A. Moya-Pérez and J. J. Nuño-Ballesteros, Topological triviality of fam-ilies of map germs from R2 to R2, J. Singul. 6 (2012), 112-123. DOI: 10.5427/jsing.2012.6i.
- J. A. Moya-Pérez and J. J. Nuño-Ballesteros, Double points in fami-lies of map germs from R2 to R3, J. Topol. Anal. (online). DOI: 10.1142/S1793525320500430.
- C. T. C. Wall, Finite determinacy of smooth map-germs, Bull. London Math.Soc. 13(6) (1981), 48-539. DOI: 10.1112/blms/13.6.481.