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SUMMARY:Slice alternating knots\, rational balls\, and lattice embeddings 
 - Brendan Owens (Glasgow) 
DTSTART:20230517T150000Z
DTEND:20230517T160000Z
UID:TALK201292@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:A fundamental problem in smooth 4-dimensional topology is to u
 nderstand which surfaces in the 4-ball can be bounded by a given classical
  knot or link\, and in particular\, whether a given knot is slice (bounds 
 a disk).  A related problem is to understand when a given 3-manifold bound
 s a rational homology 4-ball.  I will introduce these problems and then fo
 cus on the case of alternating knots and links\, and describe some recent 
 work in two  directions: 1) the determination of the sliceness of 99.9997%
  of the over 1.2 billion prime alternating knots with up to 21 crossings\,
  joint with Frank Swenton\, and 2) progress towards a conjectured characte
 risation of when the double branched cover of an alternating link bounds a
  rational ball\, joint with Josh Greene\, and using work of Greene and Jab
 uka.  The key tool is Donaldson’s diagonalisation theorem\, augmented wi
 th some Heegaard Floer theory.
LOCATION:MR13
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