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SUMMARY:A proof of Donaldson's Theorem - Samuel Muñoz Echániz\, Universi
 ty of Cambridge 
DTSTART:20211105T160000Z
DTEND:20211105T170000Z
UID:TALK165538@talks.cam.ac.uk
CONTACT:Macarena Robles-Arenas
DESCRIPTION:Donaldson’s Diagonalization Theorem states that if the inter
 section form of a closed oriented smooth 4-manifold X is definite\, then i
 t is diagonalizable over the integers. We present an outline of the origin
 al proof by Donaldson\, which appeared in his celebrated 1983 paper. \n\nT
 he proof relies on some geometric features of the moduli space of anti-sel
 f-dual (ASD) connections on an SU(2)-principal bundle over X. More concret
 ely\, it provides an oriented cobordism between X and a disjoint union of 
 complex projective spaces. This gives an estimate on the signature of X\, 
 which is the key step to the proof.  \n\nWe will introduce the ASD moduli 
 space and discuss some of its properties\, such as dimension\, its singula
 rities and its compactification. If time permits\, we will also discuss so
 me of the consequences of the theorem in Freedman’s work on 4-dimensiona
 l topology\, such as the existence of an exotic differentiable structure o
 n the 4-dimensional Euclidean space.\n
LOCATION:MR13
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