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SUMMARY:Parameterised moduli spaces of surfaces as infinite loop spaces - 
 Andrea Bianchi (Copenhagen)
DTSTART:20221130T160000Z
DTEND:20221130T170000Z
UID:TALK192380@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:We consider the E_2-algebra consisting of free loop spaces of 
 moduli spaces of Riemann surfaces with one parametrised boundary component
 \, and compute the homotopy type of its group completion: it is the produc
 t of \\Omega\\infty MTSO(2) with the free \\Omega\\infty-space generated b
 y a certain space X. This extends the classical result due to Madsen and W
 eiss to the setting of surface bundles over S^1.\n\nThe proof consists of 
 two inputs. The first input\, on which my talk will focus\, is an analysis
  of centralisers of mapping classes in generic mapping class groups Gamma_
 {g\,n}\, for g>=0 and any n>=1: this uses standard techniques of the theor
 y of mapping class groups\, such as arc complexes. The other input\, which
  I will only briefly mention\, is a generalised theory of operads with hom
 ological stability in the setting of coloured operads.\n\nThis is joint wo
 rk with Florian Kranhold and Jens Reinhold.
LOCATION:MR13
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