On Morse Theory for Piecewise Smooth Functions

被引：0
|
作者：
A. A. Agrachev
D. Pallaschke
S. Scholtes
机构：
[1] Steklov Mathematical Institute,Russian Academy of Sciences
[2] University of Karlsruhe,Institute for Statistics and Mathematical Economics
[3] University of Cambridge,Department of Engineering
来源：
Journal of Dynamical and Control Systems | 1997年 / 3卷 / 4期
关键词：
Continuous selection; critical point; nonsmooth Morse theory;
D O I：
10.1023/A:1021810206861
中图分类号：
学科分类号：
摘要：
Lower level sets of continuous selections of C2-functions defined on a smooth manifold in the vicinity of a nondegenerate critical point in the sense of [11] are studied. It is shown that the lower level set is homotopy equivalent to the join of the lower level sets of the smooth and the nonsmooth part, respectively, of the corresponding normal form. Some generalized Morse inequalities are deduced from this result.
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页码：449 / 469
页数：20
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