Друзья!

В этот вторник (21.04.26) на научном семинаре выступит Михаил Батанин. Прилагаем анонс его доклада.

Little n-disks operad and (globular) n-operads.

Globular n-operads, in general, describe n-category like structures (weak n-categories in particular). Unlike classical operads whose arities of operations are natural numbers the arities of spaces of operations of globular operads are certain basic globular pasting diagrams. There is a closed connection between classical symmetric operads and n-operads given by a pair of functors : desymmetrisation and its left adjoint called symmetrisation. In my talk I will define n-operads (more precisely certain important subcategory of n-operads sufficient for many spplications) and this adjoint pair of functors.

Then I will show that there exists a particular nice cofibrant, contractible (!) topological n-operad GJ^n with the property that its symmetrisation is isomorphic to the celebrated Fulton-Macpherson operad fm^n obtained as a compactification of moduli space of configurations of points in R^n. This result shows that homotopically the little n-disks operad is the value of the left derived functor of symmetrisation on the terminal n-operad. This should be considered as a derived version of classical Eckman-Hilton argument or as a coherence theorem for E_n-algebras. Moreover, it implies that any weak (in appropriate sense) n-category which has only one object, one arrow , one 2-cells, ..., one (n-1)-cell is exactly the same as an algebra of the little n-disks operad. Among many consequences of this theorem is a short proof of the Deligne conjecture on Hochschild cochains which I will provide if there is time.

Ждем вас 21.04.26 в 18 10 в аудитории 108.