Israel Journal of Mathematics

, Volume 105, Issue 1, pp 203-233

First online:

Choosing roots of polynomials smoothly

  • Dmitri AlekseevskyAffiliated withCenter ‘Sophus Lie’ Email author 
  • , Andreas KrieglAffiliated withInstitut für Mathematik, Universität Wien
  • , Peter W. MichorAffiliated withInstitut für Mathematik, Universität Wien
  • , Mark LosikAffiliated withSaratov State University

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We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.