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TZID:Europe/Paris
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UID:5153@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240516T110000
DTEND;TZID=Europe/Paris:20240516T120000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-65-2/
SUMMARY: (...): 3-braid knots with maximal 4-genus
DESCRIPTION:: This talk deals with the problem of determining the topologic
 al 4-genus for the special case of 3-braid knots. The 4-genus of a knot is
  the minimal genus of a "nicely" embedded surface in the 4-dimensional bal
 l with boundary the given knot. Asking whether a knot has 4-genus zero\, i
 .e. whether it bounds a disk in the 4-ball\, is a natural generalization i
 n dimension 4 of the question whether it is isotopic to the trivial knot. 
 It is one of the curiosities of low-dimensional topology that construction
 s such as finding these disks can sometimes be done in the topological cat
 egory\, but fail to work smoothly. The first examples of this phenomenon f
 ollowed Freedman's famous work on 4-manifolds.\nFour decades later\, the t
 opological 4-genus of knots - even torus knots - remains difficult to dete
 rmine. In a joint work with S. Baader\, L. Lewark and F. Misev\, we classi
 fy 3-braid knots whose topological 4-genus is maximal (i.e. equal to their
  3-genus). In the talk\, we will define the relevant terms and provide som
 e context for our results.
CATEGORIES:Séminaire,Géométrie et Topologie de Marseille
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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DTSTART:20240331T030000
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