In this paper we give a new foundational, categorical formulation for operations and
relations and objects parameterizing them. This generalizes and unifies the theory of …

In the homotopical study of spaces of smooth embeddings, the functor calculus method
(Goodwillie–Klein–Weiss manifold calculus) has opened up important connections to …

Manifold calculus is a form of functor calculus concerned with functors from some category of
manifolds to spaces. A weakness in the original formulation is that it is not continuous in the …

We study high-dimensional analogues of spaces of long knots. These are spaces of
compactly supported embeddings (modulo immersions) of ℝ m into ℝ n. We view the space …

We prove the validity over RR of a commutative differential graded algebra model of
configuration spaces for simply connected closed smooth manifolds, answering a conjecture …

The Torelli group of is the group of diffeomorphisms of fixing a disc that act trivially on. The
rational cohomology groups of the Torelli group are representations of an arithmetic …

Goodwillie calculus is a method for analyzing functors that arise in topology. One may think
of this theory as a categorification of the classical differential calculus of Newton and …

It is shown that the operad maps $ E_n\to E_ {n+ k} $ are formal over the reals for $ k\geq 2$
and non-formal for $ k= 1$. Furthermore we compute the homology of the deformation …

In this paper we describe the homology and cohomology of some natural bimodules over
the little discs operad, whose components are configurations of non-$ k $-overlapping discs …

We develop Weiss's manifold calculus in the setting of $\infty $-categories, where we allow
the target $\infty $-category to be any $\infty $-category with small limits. We will establish …