Damon, James; Gaffney, Terence Topological triviality of deformations of functions and Newton filtrations. (English) Zbl 0519.58021 Invent. Math. 72, 335-358 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 16 Documents MSC: 58C25 Differentiable maps on manifolds 58K99 Theory of singularities and catastrophe theory 57R45 Singularities of differentiable mappings in differential topology Keywords:filtration condition; jump conditions; push-off lemma; Milnor number PDF BibTeX XML Cite \textit{J. Damon} and \textit{T. Gaffney}, Invent. Math. 72, 335--358 (1983; Zbl 0519.58021) Full Text: DOI EuDML OpenURL References: [1] Arnold, V.I.: Spectral sequence for reduction of functions to normal form. Funct. Anal. and Appl.9, 251-253 (1975) · Zbl 0323.57020 [2] Arnold, V.I.: Local normal forms of functions. Invent. Math.35, 87-109 (1976) · Zbl 0336.57022 [3] Arnold, V.I.: Index of a singular point of a vector field, the Petrovski-Oleinik inequality, and mixed hodge structures. Funct. Anal. and Appl.12, 1-11 (1978) [4] Briançon, J., Speder, J.P.: La trivialite topologigue n’implique pas les conditions de Whitney. Comp. Rendust 280, (series A) 365 (1975) · Zbl 0331.32010 [5] Damon, J.: Finite determinacy and topological triviality I. Invent. Math.62, pp. 299-324 (1980) · Zbl 0489.58003 [6] Damon, J., Gaffney, T.: Topological triviality of deformations of functions and newton filtrations. preliminary announcement · Zbl 0519.58021 [7] King, H.: Topological type in families of singularities. Invent. Math.62, 1-13 (1980) · Zbl 0477.58010 [8] Kouchnirenko, A.G.: Polyedres de Newton et Nombres de Milnor. Invent. Math.32, 1-31 (1976) · Zbl 0328.32007 [9] Laufer, H.: On minimally elliptic singularities. Amer. Jour. Math.99, 1257-1295 (1977) · Zbl 0384.32003 [10] Lê D?ng Tráng, Ramanujam, C.P.: The invariance of Milnor’s number implies the invariance of topological type. Amer. Jour. Math.98, 67-78 (1976) · Zbl 0351.32009 [11] Looijenga, E.: Semi-universal deformation of a simple elliptic singularity: Part I unimodularity. Topology16, 257-262 (1977) · Zbl 0373.32004 [12] Oka, M.: On the bifurcation of the multiplicity and topology of the newton boundary. J. Math. Soc. Japan31, 435-450 (1979) · Zbl 0415.35009 [13] Teissier, B.: Cycles evanescents, sections planes, et conditions de Whitney. Singularities a Cargese. Asterisque7 and8, 285-362 (1973) · Zbl 0295.14003 [14] Timourian, J.G.: Invariance of Milnor’s number implies topological triviality. Amer. Jour. Math.99, 437-446 (1977) · Zbl 0373.32003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.