Related papers: On the delooping of (framed) embedding spaces
We study a connection between mapping spaces of bimodules and of infinitesimal bimodules over an operad. As main application and motivation of our work, we produce an explicit delooping of the manifold calculus tower associated to the space…
This paper investigates mapping spaces between enriched operads and relates these spaces to those between operadic bimodules via convenient fiber sequences. The main statements hold for simplicial operads, operads enriched in simplicial…
From a map of operads $\eta : O\rightarrow O'$, we introduce a cofibrant replacement of the operad $O$ in the category of bimodules over itself such that the corresponding model of the derived mapping space of bimodules…
The spaces of configurations of non-$k$-overlapping discs have been studied as a bimodule over the little discs operad. In fact, the spaces form a filtered operad. We define and study the induced structure on the homology.
We study a connection between a multivariable version of the Goodwillie-Weiss' calculus of functors and derived mapping spaces of k-fold bimodules over a family of operads. As our main application, under the assumption $d_{i}+3\leq n$ for…
In a recent paper, we have shown that warped time-frequency representations provide a rich framework for the construction and study of smoothness spaces matched to very general phase space geometries obtained by diffeomorphic deformations…
We study configuration spaces of framed points on oriented closed smooth manifolds. Such configuration spaces admit natural actions of the framed little discs operads, that play an important role in the study of embedding spaces of…
We record two facts on spaces of derived maps between the operads $E_d$ of little $d$-cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unitary versions of $E_d$. Secondly, all endomorphisms of $E_d$…
The paper shows that under some conditions the totalization of a cosimplicial space obtained from a multiplicative operad is a double loop space of the space of derived morphisms from the associative operad to the operad itself.
The framed little 2-discs operad is homotopy equivalent to a cyclic operad. We show that the derived modular envelope of this cyclic operad (i.e., the modular operad freely generated in a homotopy invariant sense) is homotopy equivalent to…
We study the continuous motion of smooth isometric embeddings of a planar surface in three-dimensional Euclidean space, and two related discrete analogues of these embeddings, polygonal embeddings and flat foldings without interior…
The celebrated Morlet-Burghelea-Lashof-Kirby-Siebenmann smoothing theory theorem states that the group $\mathrm{Diff}_\partial(D^n)$ of diffeomorphisms of a disc $D^n$ relative to the boundary is equivalent to…
The homotopy fiber of the inclusion from the long embedding space to the long immersion space is known to be an iterated based loop space (if the codimension is greater than two). In this paper we deloop the homotopy fiber to obtain the…
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…
We study the Disc-structure space $S^{\rm Disc}_\partial(M)$ of a compact smooth manifold $M$. Informally speaking, this space measures the difference between $M$, together with its diffeomorphisms, and the diagram of ordered framed…
Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a general class of operads in the category of spaces that satisfy certain homological stability conditions. We prove that such operads are infinite loop space…
Decomposition spaces are a class of function spaces constructed out of well-behaved coverings and partitions of unity of a set. The structure of the covering of the set determines the properties of the decomposition space. Besov spaces,…
The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…
We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…
In this paper, we give a approximation characterization, embedding properties and the duality of matrix weighted modulation spaces.