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SUMMARY:José Manuel Moreno-Fernández (Trinity College\, Dublin)
DTSTART:20210202T113000Z
DTEND:20210202T130000Z
DTSTAMP:20260419T092438Z
UID:OWHHS2021/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWHHS2021/5/
 ">A spectral sequence for tangent cohomology of algebras over algebraic op
 erads.</a>\nby José Manuel Moreno-Fernández (Trinity College\, Dublin) a
 s part of Opening Workshop (IRP Higher Homotopy Structures 2021\, CRM-Bell
 aterra)\n\n\nAbstract\nWe produce a spectral sequence that converges to th
 e operadic cohomology of a fixed algebra over an algebraic operad. Our mai
 n tool is that of filtrations arising from towers of cobrations of algebra
 s. These play the role in algebra that cell attaching maps and skeletal fi
 ltrations do for topological spaces.\n\nAs an application\, we consider th
 e rational Adams–Hilton construction on topological spaces\, where our s
 pectral sequence is multiplicative and converges to the Chas–Sullivan lo
 op product. We also consider relative Sullivan models of a fibration $p$\,
  where our spectral sequence converges to the rational homotopy groups of 
 the identity component of the space of self-fiber-homotopy equivalences of
  $p$\; and the Quillen model of a space\, where our spectral sequence conv
 erges to the homotopy groups of the classifying space of the identity comp
 onent of the self-equivalences of the space.\n\nReferences:\n\n[1] Moreno-
 Fernández\, J.\, Tamaroff\, P.\, A spectral sequence for tangent cohomolo
 gy of algebraic operads\, arXiv:2008.00876 (2020).\n
LOCATION:https://researchseminars.org/talk/OWHHS2021/5/
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