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VOL. 43 | 2006 On the topology of symmetry sets of smooth submanifolds in $\mathbb{R}^k$
Vyacheslav D. Sedykh

Editor(s) Shyuichi Izumiya, Goo Ishikawa, Hiroo Tokunaga, Ichiro Shimada, Takasi Sano


We study topology of symmetry sets, conflict sets and medial axes in the case when they have only stable singularities of corank 1. Singularities of these sets satisfy various conditions of coexistence. For example, isolated singularities and singularities forming smooth non-closed curves define a graph. If this graph is finite, then there is the following incidence relation: the sum of the local degrees of vertices of the graph is equal to the doubled number of its edges (the local degree of a vertex is the number of edges that are incident to this vertex; loops are counted twice). We give many-dimensional generalizations of this relation for sets mentioned above. These generalizations follow from some general facts on coexistence of wave front singularities found recently by the author.


Published: 1 January 2006
First available in Project Euclid: 3 January 2019

zbMATH: 1148.58017
MathSciNet: MR2325148

Digital Object Identifier: 10.2969/aspm/04310401

Rights: Copyright © 2006 Mathematical Society of Japan


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