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SUMMARY:Maurer-Cartan moduli and higher Riemann-Hilbert correspondence(s)\
; joint with J. Chuang and J. Holstein
DTSTART;VALUE=DATE-TIME:20171010T090000Z
DTEND;VALUE=DATE-TIME:20171010T100000Z
DTSTAMP;VALUE=DATE-TIME:20210417T102631Z
UID:indico-event-2834@indico.math.cnrs.fr
DESCRIPTION:« Seminar on homological algebra »\n\n \n\nA Maurer-Carta
n (MC) element in a differential graded (dg) algebra A is an odd element x
satisfying the equation dx+x2=0. The group of invertible elements of A ac
ts on MC element by gauge transformations: g(x):=gxg-1-dgg-1. MC eleme
nts are an abstraction of the notion of a flat connection and are fundamen
tal in many problems of homological algebra\, deformation theory\, differe
ntial geometry etc.\n\n \n\nThere is a notion of a (Sullivan) homotopy of
MC elements: two such are homotopic if they could be extended to a family
over the de Rham algebra on the interval R[x\,dx]. A fundamental result (
over 40 years old) due to Schlessinger and Stasheff (SS) states that (unde
r certain assumptions) two MC elements are gauge equivalent if an only if
they are homotopic.\n\n \n\nThere is also another notion of homotopy of M
C elements\, based on the singular cochain complex of the interval\, and a
corresponding SS type theorem.\n\n \n\n\n\n \n\nhttps://indico.math.cnr
s.fr/event/2834/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/2834/
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