Related papers: $A_\infty$ structures and Massey products
Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of…
In this paper, we introduce a new class of structured spaces which is locally modeled by Costello's L-infinity spaces. This provides an alternative approach to study the derived geometric structures in the algebraic, analytic, or smooth…
We elaborate on an idea of M. Abouzaid of equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an $A_\infty$-algebra. This is a variation on K. Fukaya's definition of…
We consider the space $\Lambda M:=H^1(S^1,M)$ of loops of Sobolev class $H^1$ of a compact smooth manifold $M$, the so-called free loop space of $M$. We take quotients $\Lambda M/G$ where $G$ is a finite subgroup of $O(2)$ acting by linear…
There have recently been several developments in synthetic mathematics using extensions of dependent type theory with univalence and higher inductive types: simplicial homotopy type theory, synthetic algebraic geometry and synthetic Stone…
Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…
A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.
We give a quick method of constructing strong homotopy associative algebra, namely, the higher derived product construction. This method is associative analogue of classical higher derived bracket construction in the category of Loday…
The notion of a dual polyhedral product is introduced as a generalization of Hovey's definition of Lusternik-Schnirelmann cocategory. Properties established from homotopy decompositions that relate the based loops on a polyhedral product to…
Given a bundle of chain complexes, the algebra of functions on its shifted cotangent bundle has a natural structure of a shifted Poisson algebra. We show that if two such bundles are homotopy equivalent, the corresponding Poisson algebras…
The homotopy category of $N_\infty$ operads is equivalent to a finite lattice, and as the ambient group varies, there are various image constructions between these lattices. In this paper, we explain how to lift this algebraic structure…
In this paper we analyse for a $G$-$C^{*}$-algebra $A$ to which extent one can calculate the $K$-theory of the reduced crossed product $K(A\rtimes_{r}G)$ from the $K$-theory spectrum $K(A)$ with the induced $G$-action. We also consider some…
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…
Higher bundles are homotopy coherent generalisations of classical fibre bundles. They appear in numerous contexts in geometry, topology and physics. In particular, higher principal bundles provide the geometric framework for higher-group…
For $M$ a compact Riemannian manifold Brandenbursky and Marcinkowski constructed a transfer map $H_b^*(\pi_1(M))\to H_b^*(Homeo_{vol,0}(M))$ and used it to show that for certain $M$ the space $\overline{EH}_b^3(Homeo_{vol,0}(M))$ is…
The aim of this paper is to give relations between the category of finetely generated graded modules over the homogeneized Weyl algebra $B_{n}$, the finetely generated modules over the Weyl algebra $A_{n}$ and the finetely generated graded…
We bring spaces over the classifying space $BS^1$ of the circle group $S^1$ to persistence theory via the singular cohomology with coefficients in a field. Then, the {\it cohomology} interleaving distance (CohID) between spaces over $BS^1$…
We present a classification of homogeneous star products on duals of Lie algebroids in terms of the second Lie algebroid cohomology. Moreover, we extend this classification to projectable star products, i.e., to quantizations compatible…
Homotopy links have proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy links of a stratified simplicial set. For many purposes, in…
Primary cohomology operations, i.e., elements of the Steenrod algebra, are given by homotopy classes of maps between Eilenberg--MacLane spectra. Such maps (before taking homotopy classes) form the topological version of the Steenrod…