Related papers: Strong minimal model theorem and Massey products

We show that in the bounded cohomology of non-abelian free groups the Massey triple product is always trivial when the second factor is represented by the coboundary of a decomposable quasi-morphism. We also show that in the bounded…

We study the equivalence between infinitesimal Torelli theorem for smooth hypersurfaces in rational homogeneous varieties with Picard number one and the theory of generalized Massey products. This equivalence shows that the differential of…

This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…

We analyse volume-preserving actions of product groups on Riemannian manifolds. To this end, we establish a new superrigidity theorem for ergodic cocycles of product groups ranging in linear groups. There are no a priori assumptions on the…

According to a 1975 result of T. Kaijser, if some nonvanishing product of hidden Markov model (HMM) stepping matrices is subrectangular, and the underlying chain is aperiodic, the corresponding $\alpha$-chain has a unique invariant limiting…

In this paper, we show that the existence of two sequences of Massey iterated product containing zero in the cohomology of a 1-connected CW complex of finite type $X$ directly bears on the unbounded growth of the Betti numbers of the free…

We study the relationship between the higher Massey products on the cohomology $H$ of a differential graded algebra, and the $A_\infty$ structures induced on $H$ via homotopy transfer techniques.

Consider the minimal renormalizable extension of the Standard Model with purely dimensionless couplings, successful electroweak symmetry breaking (via the Coleman-Weinberg mechanism) and a see-saw mechanism for neutrino mass: we will call…

We construct an $A_{\infty}$-structure on the Ext-groups of hermitian holomorphic vector bundles on a compact complex manifold. We propose a generalization of the homological mirror conjecture due to Kontsevich. Namely, we conjecture that…

Let $p$ be a prime number, let $G$ be a profinite group, let $\theta\colon G\to \mathbb{Z}_p^{\times}$ be a continuous character, and for all $n\geq 1$ write $\mathbb{Z}/p^n\mathbb{Z}(1)$ for the twist of $\mathbb{Z}/p^n\mathbb{Z}$ by the…

Let p be a prime number and F a field containing a root of unity of order p. We relate recent results on vanishing of triple Massey products in the mod-p Galois cohomology of F, due to Hopkins, Wickelgren, Minac, and Tan, to classical…

We prove that, for all fields $F$ of characteristic different from $2$ and all $a,b,c\in F^\times$, the mod $2$ Massey product $\langle a,b,c,a \rangle$ vanishes as soon as it is defined. For every field $F_0$, we construct a field $F$…

Handling curved $ A_\infty $-deformations is challenging and defining their derived categories seems impossible. In this paper, we show how to welcome the curvature and build derived categories despite the apparent difficulties. We…

Let $\F$ be a collection of subsets of $\Z_+$ and $(X,T)$ be a dynamical system. $x\in X$ is $\F$-recurrent if for each neighborhood $U$ of $x$, $\{n\in\Z_+:T^n x\in U\}\in \F$. $x$ is $\F$-product recurrent if $(x,y)$ is recurrent for any…

The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, that is, those that have finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic…

Associated to every connected, topological space $X$ there is a Hopf algebra - the Pontrjagin ring of the based loop space of the configuration space of two points in X. We prove that this Hopf algebra is not a homotopy invariant of the…

We prove a Khintchine-type recurrence theorem for pairs of endomorphisms of a countable discrete abelian group. As a special case of the main result, if $\Gamma$ is a countable discrete abelian group, $\varphi, \psi \in End(\Gamma)$, and…

Let $\|x\|$ denote the distance from $x\in\mathbb{R}$ to the nearest integer. In this paper, we prove an existence and density statement for matrices $\boldsymbol{A}\in\mathbb{R}^{m\times n}$ satisfying…

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…

We show that on a compact complex surface all Massey products of cohomology classes in degree one vanish beyond length three. Dually, the real Malcev completion of the fundamental group is homogeneously presented by quadratic and cubic…