TOPOLOGICAL TRIVIALITY AND VERSALITY FOR SUBGROUPS OF A AND K .2. SUFFICIENT CONDITIONS AND APPLICATIONS

被引:25
作者
DAMON, J
机构
[1] Department of Mathematics, University of North Carolina, Chapel Hill, NC
关键词
D O I
10.1088/0951-7715/5/2/005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Many different questions involving the local structure of mappings, the varieties they define, and their local bifurcations are studied by introducing a group of germs of diffeomorphisms, so that the equivalence via elements of the group captures the desired properties. Then, the local classification of mappings, their local determination by finite parts of their Taylor expansions, and the construction of finite parameter families exhibiting all of their perturbation behaviour can be frequently carried out following the original ideas of Thom and Mather. However, the presence of moduli parametrizing continuous change in the equivalences classes forces one to substitute a corresponding topological equivalence, so the results no longer apply. In this paper we shall prove theorems which do solve these problems for the topological analogues of a wide variety of equivalence relations. These results are given by infinitesimal conditions but relative to algebraic filtration conditions on the tangent spaces to the group of diffeomorphisms and to the spaces of germs. These results are applied to a number of problems involving the classification of finite map germs, equivariant bifurcation problems, and the equivalence of germs preserving varieties.
引用
收藏
页码:373 / 412
页数:40
相关论文
共 41 条
[1]   WAVE FRONT EVOLUTION AND EQUIVARIANT MORSE LEMMA [J].
ARNOLD, VI .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1976, 29 (06) :557-582
[2]  
BRUCE JW, 1985, P LOND MATH SOC, V50, P535
[3]   CRITICAL-POINTS OF FUNCTIONS ON ANALYTIC VARIETIES [J].
BRUCE, JW ;
ROBERTS, RM .
TOPOLOGY, 1988, 27 (01) :57-90
[4]  
BRUCE JW, 1984, J LOND MATH SOC, V30, P551
[6]  
DAMON J, 1983, P SYMP PURE MATH, V40, P233
[8]   FINITE DETERMINACY AND TOPOLOGICAL TRIVIALITY .1. [J].
DAMON, J .
INVENTIONES MATHEMATICAE, 1980, 62 (02) :299-324
[9]   TOPOLOGICAL TRIVIALITY OF DEFORMATIONS OF FUNCTIONS AND NEWTON FILTRATIONS [J].
DAMON, J ;
GAFFNEY, T .
INVENTIONES MATHEMATICAE, 1983, 72 (03) :335-358
[10]  
DAMON J, 1983, P SYMP PURE MATH, V40, P267