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UID:6513@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210311T140000
DTEND;TZID=Europe/Paris:20210311T150000
DTSTAMP:20250118T133159Z
URL:https://www.i2m.univ-amu.fr/evenements/lipschitz-normally-embedding-an
 d-moderately-discontinuous-homology/
SUMMARY:Xuan Viet Nhan Nguyen (Basque Center for Applied Mathematics (BCAM)
 \, Spain): Lipschitz Normally Embedding and Moderately Discontinuous Homol
 ogy
DESCRIPTION:Xuan Viet Nhan Nguyen: In [1] J. Bobadilla et al introduced a h
 omology called Moderately Discontinuous homology (MD-homology) in order to
  capture the homology of a given germ after collapsing with certain speed.
  A subanalytic germ $(X\, 0)$ is called LNE (Lipschitz normally embedded) 
 if the inner metric and the outer metric on $(X\,0)$ are bi-Lipschitz equi
 valent. The identity map on $(X\,0)$ induces homomorphisms between groups 
 of MD-homologies of $(X\,0)$ with respect to these two metrics. It is easy
  to check that if $(X\,0)$ is LNE then these homomorphisms are isomorphic.
  It is asked in the paper that suppose the homomorphisms induced by the id
 entity map are isomorphisms at every point on $(X\,0)$\, is $(X\,0)$ LNE? 
 We will present an example showing that in general\, the answer is negativ
 e.\n[1] J. Bobadilla\, S. Heinze\, M. Pe Pereira\, and J.E. Sampaio\, Mode
 rately discontinuous homology\, (2020)\, https://arxiv.org/abs/1910.12552 
 (preprint).\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Xuan_Viet_Nhan_Nguyen.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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