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Methods for Classification of Singularities

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2165)

Abstract

In this chapter we will recall the methods which were introduced by Thom [Le] and especially Mather [MIII, MVI] to classify germs of mappings under various equivalence groups by reducing to the induced actions of Lie groups on jet spaces. This involves using finite determinacy results and Mather’s geometric lemma for actions of Lie groups. This was considerably strengthened by the much improved order of determinacy results from the stronger method of unipotent groups due to Bruce-Du Plessis-Wall [BDW]. These results will be appropriately adapted to apply to our situation.

Keywords

  • Vector Field
  • Normal Form
  • Topological Method
  • Unipotent Group
  • Abstract Classification

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    This software package uses an early version of Maple [M].

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Damon, J., Giblin, P., Haslinger, G. (2016). Methods for Classification of Singularities. In: Local Features in Natural Images via Singularity Theory. Lecture Notes in Mathematics, vol 2165. Springer, Cham. https://doi.org/10.1007/978-3-319-41471-3_6

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