Subanalytic Bundles and Tubular Neighbourhoods of Zero-Loci

2003/07/31 by Vishwambhar Pati
Mathematics · #math.AG #math.GT #msc:32B20 #msc:32C05 #msc:14P15 #msc:14P25

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 3, August 2003, pp. 251-279 · 29 pages

arxiv created 2003/12/05 · arxiv updated 2009/11/30

Abstract

We introduce the natural and fairly general notion of a subanalytic bundle (with a finite dimensional vector space P of sections) on a subanalytic subset X of a real analytic manifold M, and prove that when M is compact, there is a Baire subset U of sections in P whose zero-loci in X have tubular neighbourhoods, homeomorphic to the restriction of the given bundle to these zero-loci.

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