Cotangent complex of the topological E_n - operads (part II)

Thời gian: 09h00, thứ năm, ngày 2/3/2023.

Địa điểm: Phòng 507, nhà A6.

Tóm tắt: Kontsevich predicted the existence of an exact sequence relating the cotangent complex of an $E_n$ - algebra and its Hochschild complex. This was proved by Francis and Lurie, when working in good stable base categories (e.g. chain complexes, spectra). On the other hand, in any unstable category (typically, category of topological spaces), such a comparison has not yet been considered. We state and prove three versions of Kontsevich conjecture for $E_n$ - operads and $E_n$ - algebras, in the framework of topological settings. Our approach is a new one, based on the construction of twisted arrow categories of operads. For an application, we illustrate a concrete relation between Hochschild cohomology and the deformation theory of $dg E_n$ - operads