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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Slice alternating knots\, rational balls\, and lat
tice embeddings - Brendan Owens (Glasgow)
DTSTART;TZID=Europe/London:20230517T160000
DTEND;TZID=Europe/London:20230517T170000
UID:TALK201292AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/201292
DESCRIPTION:A fundamental problem in smooth 4-dimensional topo
logy is to understand which surfaces in the 4-ball
can be bounded by a given classical knot or link\
, and in particular\, whether a given knot is slic
e (bounds a disk). A related problem is to unders
tand when a given 3-manifold bounds a rational hom
ology 4-ball. I will introduce these problems and
then focus on the case of alternating knots and l
inks\, and describe some recent work in two direc
tions: 1) the determination of the sliceness of 99
.9997% of the over 1.2 billion prime alternating k
nots with up to 21 crossings\, joint with Frank Sw
enton\, and 2) progress towards a conjectured char
acterisation of when the double branched cover of
an alternating link bounds a rational ball\, joint
with Josh Greene\, and using work of Greene and J
abuka. The key tool is Donaldsonâ€™s diagonalisatio
n theorem\, augmented with some Heegaard Floer the
ory.
LOCATION:MR13
CONTACT:Oscar Randal-Williams
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