Related papers: Geometric and algebraic aspects of 1-formality

The strong homotopy Lie algebra, controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is constructed. Isomorphism of the cohomology of this strong homotopy Lie algebra with the classical…

We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…

We define the Hochschild (co)homology of a ringed space relative to a locally free Lie algebroid. Our definitions mimic those of Swan and Caldararu for an algebraic variety. We show that our (co)homology groups can be computed using…

Fold maps are smooth maps at each singular point of which it is represented as the product map of a Morse function and the identity map. Round fold maps are, in short, such maps the sets of all singular points of which are embedded…

Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…

We completely characterize the pairs of connected Lie groups $G > K$ such that $\mathrm{rank}(G) - \mathrm{rank}(K) = 1$ and the left action of $K$ on $G/K$ is equivariantly formal. The analysis requires us to correct and extend an existing…

This is a survey on cohomogeneity one manifolds with positive curvature. We discuss the known examples of this type and their geometry and the functions that describe the metric. We also describe the classification of cohomogeneity one…

If M is a manifold with an action of a group G, then the homology group H_1(M,Q) is naturally a Q[G]-module, where Q[G] denotes the rational group ring. We prove that for every finite group G, and for every Q[G]-module V, there exists a…

We show a Gottlieb element in the rational homotopy of a simply connected space $X$ implies a structural result for the Sullivan minimal model, with different results depending on parity. In the even-degree case, we prove a rational…

While small deformations of K\"ahler manifolds are K\"ahler too, we prove that the cohomological property to be $\mathcal{C}^\infty$-pure-and-full is not a stable condition under small deformations. This property, that has been recently…

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient…

For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…

Each choice of a K\"ahler class on a compact complex manifold defines an action of the Lie algebra $\slt$ on its total complex cohomology. If a nonempty set of such K\"ahler classes is given, then we prove that the corresponding…

Let M be a compact, connected and simply-connected Riemannian manifold, and suppose that G is a compact, connected Lie group acting on M by isometries. The dimension of the space of orbits is called the cohomogeneity of the action. If the…

$\newcommand{\OO}[1]{\mathcal{O}_{#1}}\newcommand{\GG}{\mathcal{G}}\newcommand{\End}{\mathrm{End}}\newcommand{\O}{\mathcal{O}}$Let $K/F$ be a quadratic extension of non-Archimedean local fields of characteristic not equal to 2, with rings…

This article records basic topological, as well as homological properties of the space of homomorphisms Hom(L,G) where L is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If L is a free abelian group of…

A hyperk\"ahler manifold is defined as a Riemannian manifold endowed with three covariantly constant complex structures that are quaternionically related. A twistor space is characterized as a holomorphic fiber bundle $p: \mathcal{Z}…

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

In this article, we use Harrison cohomology to provide a framework for commutative deformations. In particular, Kontsevich's result that formality of (the Hochschild complex of) an associative algebra implies its deformability is adapted…

Let us consider a compact oriented riemannian manifold M without boundary and of dimension n=4k. The signature of M is defined as the signature of a given quadratic form Q. Two different products could be used to define Q and they render…