We use mixed Hodge theory to show that the functor of singular chains with rational
coefficients is formal as a lax symmetric monoidal functor, when restricted to complex …

We show that the integer cohomology rings of the moduli spaces of stable rational marked
curves are Koszul. This answers an open question of Manin. Using the machinery of Koszul …

Using a variant of the Boardman–Vogt tensor product, we construct an action of the
Grothendieck–Teichmüller group on the completion of the little n‐disks operad E n. This …

We compute some differentials of Sinha's spectral sequence for cohomology of the space of
long knots modulo immersions in codimension one, mainly over a field of characteristic 2 or …

We introduce framed formal curves, which are formal algebraic curves with boundary
components parametrized by the punctured formal disk. We study the moduli space of nodal …

Planar non-formality of the little discs operad in characteristic two | The Quarterly Journal of
Mathematics | Oxford Academic Skip to Main Content Advertisement Oxford Academic …

Abstract The Swiss-Cheese operads, which encode actions of algebras over the little n-
cubes operad on algebras over the little-cubes operad, comes in several variants. We prove …

This chapter aims to survey applications of the little discs operads which were motivated by
the works of Kontsevich and Tamarkin on the deformation-quantization of Poisson manifolds …

We construct a canonical chain of formality quasiisomorphisms for the operad of chains on
framed little disks and the operad of chains on little disks. The construction is done in terms …

An algebraic structure A (eg an associative algebra, a commutative algebra, an operad, etc.)
in the category of chain complexes is said to be formal if it is connected to its homology H (A) …