BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Juan Ballesteros (University of Valencia\, Spain & UFPB\, Brazil)
DTSTART:20210624T190000Z
DTEND:20210624T200000Z
DTSTAMP:20260423T021444Z
UID:UFPB/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UFPB/22/">Co
 mbinatorial models in the topological classification of singularities of m
 appings</a>\nby Juan Ballesteros (University of Valencia\, Spain & UFPB\, 
 Brazil) as part of Seminários de Matemática da UFPB\n\n\nAbstract\nThe t
 opological classification of finitely determined map germs f from $(R^n\,0
 )$ to $(R^p\,0)$ is discrete (by a theorem due to R. Thom)\, hence we want
  to obtain combinatorial models which codify all the topological informati
 on of the map germ. According to Fukuda's work\, the topology of such germ
 s is determined by the link\, which is obtained by taking the intersection
  of the image of f with a small enough sphere centered at the origin. If $
 f^{-1}(0)=\\left\\{0\\right\\}$\, then the link is a topologically stable 
 map from $S^{n-1}$ to $S^{p-1}$ (or stable if $(n\,p)$ are nice dimensions
 ) and f is topologically equivalent to the cone of the link. When $f^{-1}(
 0)$ is not equal to $\\left\\{0\\right\\}$\, the situation is more complic
 ated. We analyze the particular case of mappings from $R^2$ to $R^3$\, whe
 re the link is a doodle (a closed curve on the sphere with only transverse
  double points) and the combinatorial model is provided by the Gauss word.
  We will review some recent results about topological classification\, sin
 gularities of ruled surfaces\, topological triviality of families and topo
 logical finite determinacy.\n
LOCATION:https://researchseminars.org/talk/UFPB/22/
END:VEVENT
END:VCALENDAR