Related papers: On the delooping of (framed) embedding spaces
In this paper we give a description of the first order deformation space of a regular embedding of reduced algebraic schemes. We compare our result with results of Ran (in particular [Ran, Prop. 1.3]).
We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichm\"uller space, we consider whether they are quasi-isometric embeddings with respect to…
For $L \hookrightarrow X$ a Lagrangian embedding associated with a real homogeneous space, we construct the moduli space of stable holomorphic discs mapping to $(X,L)$ as an orbifold with corners equipped with a group action. Some essential…
Our aim is to introduce and advocate non-$\Sigma$ (non-symmetric) modular operads. While ordinary modular operads were inspired by the structure of the moduli space of stable complex curves, non-$\Sigma$ modular operads model surfaces with…
The framed n-discs operad fD_n is studied as semidirect product of SO(n) and the little n-discs operad. Our equivariant recognition principle says that a grouplike space acted on by fD_n is equivalent to the n-fold loop space on a…
One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…
This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the…
We present two methods to interpolate between two given rigid body displacements. Both are based on linear interpolation in the ambient space of well-known curved point models for the group of rigid body displacements. The resulting motions…
The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…
In this expository paper we give an elementary, hands-on computation of the homology of the little disks operad, showing that the homology of a $d-fold loop space is a Poisson algebra. One aim is to familiarize a greater audience with…
Embedding models trained separately on similar data often produce representations that encode stable information but are not directly interchangeable. This lack of interoperability raises challenges in several practical applications, such…
Given an acyclic map $X\to Y$ of closed manifolds dimension $d$, we study the relationship between the embeddings of $Y$ in $S^{n}$ with those of $X$ in $S^{n}$ when $n-d \ge 3$. The approach taken here is to first solve the Poincar\'e…
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology…
The category of differential graded operads is a cofibrantly generated model category and as such inherits simplicial mapping spaces. The vertices of an operad mapping space are just operad morphisms. The 1-simplices represent homotopies…
In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a…
In recent years, foundation models have significantly advanced data-driven systems across various domains. Yet, their underlying properties, especially when functioning as feature extractors, remain under-explored. In this paper, we…
We show upper and lower embeddings of $\alpha_1$-modulation spaces in $\alpha_2$-modulation spaces for $0 \leq \alpha_1 \leq \alpha_2 \leq 1$, and prove partial results on the sharpness of the embeddings.
We study the homotopy derivations of the framed little discs operads, which correspond to the homotopy derivations of the BV2n operads. By extending a result by Willwacher about the homotopy derivations of the en operads we show that the…
We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective)…
This note is dedicated to the study of a Hopf module structures on the space of framed chord diagrams and framed graphs. We also introduce a framed version of the chromatic polynomial and propose two methods to construct framed weight…