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Finite Determinacy

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Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 357)

Abstract

We prove Mather’s theorem that germs with finite \(\mathscr {A}\)-codimension are finitely determined (determined up to \(\mathscr {A}\)-equivalence by a finite Taylor polynomial) along with later improvements due to Gaffney, du Plessis, Bruce and Wall. We give a brief discussion of unipotent algebraic groups in preparation for the theorem of Bruce, du Plessis and Wall on finite determinacy relative to unipotent subgroups of the group \(\mathscr {A}\). The chapter ends with a section on the method of complete transversals for classifying map-germs.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Departament de MatemàtiquesUniversitat de ValènciaBurjassotSpain

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