Seminar of AG Laboratory: Boris Shoikhet (Antwerpen)
Event ended
26th of January 2018, 5:00 p.m., room 306
It was proven by D.Tamarkin that the shifted deformation complex of an n-algebra X in complexes of vector spaces over a field of characteristic 0, Def(X)[-n], is a homotopy (n+1)-algebra for n>1. The latter deformation complex for n=1 is the Hochschild complex of an associative algebra X, it is a homotopy 2-algebra by so-called Deligne conjecture. This statement admits several proofs, but all of them use transcendental methods.
Tamarkin's observation was that for n>=2, the statement can be proven algebraically, without any transcendental methods.
We consider more general deformation complexes Def(e_n-->O)[-n] where O is another operad, and we deform a map f: e_n-->O. (This complex becomes Def(X)[-n] for O=End(X), the End-operad).
We prove that the latter more general complex is also a homotopy (n+1)-algebra, for any O and f, in a canonical way.