Related papers: $L_\infty$ and $A_\infty$ structures: then and now
Suppose $X$ is a locally solid lattice ring. It is known that there are three classes of bounded group homomorphisms on $X$ whose topological structures make them again topological rings. In this note, we consider lattice structure on them;…
The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…
The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…
This paper is a survey of our previous works on open-closed homotopy algebras, together with geometrical background, especially in terms of compactifications of configuration spaces (one of Fred's specialities) of Riemann surfaces,…
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…
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…
The study of higher tangential structures, arising from higher connected covers of Lie groups (String, Fivebrane, Ninebrane structures), require considerable machinery for a full description, especially for connections to geometry and…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…
Building on Kadeishvili's original theorem inducing $A_\infty$-algebra structures on the homology of dg-algebras, several directions of algorithmic research in $A_\infty$-algebras have been pursued. In this paper we will survey work done on…
We detect higher order Whitehead products on the homology $H$ of a differential graded Lie algebra $L$ in terms of higher brackets in the transferred $L_\infty$ structure on $H$ via a given homotopy retraction of $L$ onto $H$.
The halo structure originated in nuclear physics but is now encountered more widely. It appears in loosely bound, clustered systems where the spatial extension of the system is significantly larger than that of the binding potentials. A…
L-Infinity structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of $L_n$ and $L_{\infty}$ structures on…
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
This paper explores the relation between the structure of fibre bundles akin to those associated to a closed almost nonnegatively sectionally curved manifold and rational homotopy theory.
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
We look at two examples of homotopy Lie algebras (also known as L_{\infty} algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree…
The currently standard theory of cosmic structure formation posits that the present-day clumpy appearance of the universe developed through gravitational amplification of the matter density fluctuations that are generated in the very early…
Persistent homology typically studies the evolution of homology groups $H_p(X)$ (with coefficients in a field) along a filtration of topological spaces. $A_\infty$-persistence extends this theory by analysing the evolution of subspaces such…
In this work, we propose a novel approach to the homotopy transfer procedure starting from a set of homotopy data such that the first differential complex is a differential graded module over the second one. We show that the module…