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SUMMARY:An infinity Operad of Normalized Cacti
DTSTART:20201013T101500
DTEND:20201013T111500
DTSTAMP:20260407T195358Z
UID:102c16702839db397f20de83873a2a82814ac8e45f5f3b3956c0e1a9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Luciana Bonatto\, University of Oxford\nGluing surfaces along 
 their boundaries allows us to define composition laws that have been used 
 to define cobordism categories\, as well as operads and props associated t
 o surfaces. These have played an important role in recent years\, for exam
 ple in constructing topological field theory or computing the homology of 
 the moduli space of Riemann surfaces.\n\nNormalized cacti are a graphical 
 model for the moduli space of genus 0 oriented surfaces. They are endowed 
 with a composition that corresponds to glueing surfaces along their bounda
 ries\, but this composition is not associative. By introducing a new topol
 ogical operad of bracketed trees\, we show that this operation is associat
 ive up-to all higher homotopies and that normalized cacti form an $\\infty
 $-operad. In particular\, this provides one of the few examples in the lit
 erature of infinity operads that are not a nerve of an actual operad.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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