Erik Lindell
IMJ-PRG (Paris 6)
https://sites.google.com/view/eriklindellmath/
Date(s) : 02/05/2024 iCal
11 h 00 min - 12 h 00 min
The cohomology of Aut(Fn), the automorphism group of a free group on n generators, has been studied by many authors. In particular, much progress has been made concerning its stable cohomology, i.e. the cohomology in degrees sufficiently low compared to n. It was proven by Galatius that the stable cohomology groups with coefficients in Q are trivial. With coefficients in tensor powers of the first rational homology of Fn, or its first rational cohomology, the stable cohomology groups were independently computed by Djament and Vespa (using functor homology methods) and by Randal-Williams (by extending the methods of Galatius). For mixed tensor powers of these coefficients (« bivariant » twisted coefficients), a conjectural description was given by Djament. Furthermore, Kawazumi and Vespa proved that the collection of stable cohomology groups with all different bivariant twisted coefficients has the structure of a so-called « wheeled PROP » and rephrased the conjecture of Djament in these terms. Recently, I managed to confirm this conjecture, by essentially pushing the methods of Randal-Williams a bit further. In this talk I will review these results and, if time permits, sketch my proof of the conjecture.
Emplacement
Salle de séminaire de l'I2M à St Charles
Catégories