The operad associated to a crossed simplicial group (Artem SEMIDETNOV, UNIGE)

16.06.2026 15:30 – 16:30

By the Kan–Thurston theorem, any connected homotopy type is realizable as (BG)+ for a discrete group G. Deep results of Barratt–Priddy–Quillen, Galatius, Madsen–Weiss, and others concretely identify the homotopy types of (BG∞)+ for families such as Gn = Σn+1,Bn+1, Aut(Fn),GLn(K). However, these methods do not extend to other natural families, such as the homotopy braids Gn = hBn+1, for which (BhB∞)+ remains unexplored.
In this talk I will present an operadic enhancement of the crossed simplicial groups of Loday–Fiedorowicz. To each operadic crossed simplicial group one associates an operad in groupoids, recovering the E∞- and E2-operads in the symmetric and braid cases. The main applications are a generalized bar construction specializing to the classical symmetric and braided variants, and an identification of the associated group-completed monads with Barratt–Priddy–Quillen type spaces—providing a new approach to (BhB∞)+, (BΣ∞)+, and (BB∞)+.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Groupes de Lie et espaces de modules"

Depending on the G7 situation, the seminar might be moved to Zoom. More information on Friday June 12.

entrée libre