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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:An approach to the four colour theorem via Donalds
on- Floer theory - Tomasz Mrowka (Massachusetts In
stitute of Technology)
DTSTART;TZID=Europe/London:20170816T120000
DTEND;TZID=Europe/London:20170816T130000
UID:TALK75811AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/75811
DESCRIPTION:This talk will outline an approach to the fo
ur colour theorem using a variant of Donaldson-Flo
er theory.

To each trivalent graph embedde
d in 3-space\, we associate an instanton homology
group\, which is a finite-dimensional Z/2 vector s
pace. Versions of this instanton homology can be c
onstructed based on either SO(3) or SU(3) represen
tations of the fundamental group of the graph comp
lement. \; For the SO(3) instanton homology th
ere is a non-vanishing theorem\, proved using tech
niques from 3-dimensional topology: if the graph i
s bridgeless\, its instanton homology is non-zero.
It is not unreasonable to conjecture that\, if th
e graph lies in the plane\, the Z/2 dimension of t
he SO(3) homology is also equal to the number of T
ait colourings which would imply the four colour t
heorem. \; This is joint work with P
eter Kronheimer.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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