• Subanalytic bundles and tubular neighbourhoods of zero-loci

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/113/03/0251-0279

    • Keywords

       

      Subanalytic set; subanalytic bundle; Strong Whitney stratification; Verdier stratification; tubular neighbourhood; zero-locus of subanalytic bundle; stratified transversality

    • Abstract

       

      We introduce the natural and fairly general notion of a subanalytic bundle (with a finite dimensional vector spaceP of sections) on a subanalytic subsetX of a real analytic manifoldM, and prove that whenM is compact, there is a Baire subsetU of sections inP whose zero-loci inX have tubular neighbourhoods, homeomorphic to the restriction of the given bundle to these zero-loci.

    • Author Affiliations

       

      Vishwambhar Pati1

      1. Stat-Math Unit, Indian Statistical Institute, R.V. College Post, Bangalore - 560 059, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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