November 14,  2025

on-line on zoom

Meeting ID: 939 3295 1831
Passcode: 696997

•  11:00-11:50 Claudio Murolo (Universite d'Aix-Marseille) Smooth Whitney Fibering Conjecture, Part I (Background, applications, and the depth(X) = 1 case)

  Abstract:  This presentation, which will be given in two parts, has the aim of presenting the smooth version of the Whitney fibering conjecture (J. Diff. Geom. 1965) and the applications that motivated this work. This is a joint paper with D. Trotman and A. du Plessis (JLMS, Dec. 2024).
  
  The smooth version of the conjecture consists of an improvement of Thom-Mather's first isotopy theorem for Whitney stratifications and, more precisely, of proving that Thom-Mather's theorem can be obtained by providing a local foliated structure with tangent spaces varying continuously near the singularities. We prove this for (c)-regular Bekka stratifications, which are more general.
  
  The proofs involve the integration of carefully chosen, controlled distributions of vector fields. The first part is therefore devoted to a general presentation of the problem in the smooth context and to citing future applications, followed by a detailed exposition of all the ingredients and techniques necessary to establish this theorem, proved first for the case of a stratum of depth 1 in its stratification. This first talk is necessary to understand most of the statements and proofs of the second part.
  
  The second part will be devoted to the proof of the general case and our most significant applications. In particular:  
  
  - the existence of local wing structures near the singularities for (c)-regular Bekka stratifications, necessary to prove the general case;
  - a horizontally-\(\mathcal{C}^1\) version of Thom-Mather's first isotopy theorem;
  - the density of the subset of strongly topologically stable maps in the subspace of quasi-proper maps of \(\mathcal{C}^\infty\) (N,P) between two manifolds   
    (an improvement on a theorem of Mather).