Related papers: On non-formality of homogeneous spaces

Several large classes of homogeneous spaces are known to be formal---in the sense of Rational Homotopy Theory. However, it seems that far fewer examples of non-formal homogeneous spaces are known. In this article we provide several…

We provide examples of homogeneous spaces which are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric…

Formality is a topological property, defined in terms of Sullivan's model for a space. In the simply-connected setting, a space is formal if its rational homotopy type is determined by the rational cohomology ring. In the general setting,…

Let $X$ be a nilpotent space such that there exists $p\geq 1$ with $H^p(X,\mathbb Q) \ne 0$ and $H^n(X,\mathbb Q)=0$ if $n>p$. Let $Y$ be a m-connected space with $m\geq p+1$ and $H^*(Y,\mathbb Q)$ is finitely generated as algebra. We…

We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms…

Let $X$ be a nilpotent space such that there exists $N\geq 1$ with $H^N(X,\mathbb Q) \ne 0$ and $H^n(X,\mathbb Q)=0$ if $n>N$. Let $Y$ be a m-connected space with $m\geq N+1$ and $H^*(Y,\mathbb Q)$ is finitely generated as algebra. We…

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…

\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…

Let $X$ be a simply connected path connected topological space which is formal in the sense of rational homotopy theory. Let $Y=X\cup_\alpha\mathbb{D}^{n}$ where $\alpha:\mathbb{S}^{n-1}\to X$ is a non-torsion element. Then we obtain a…

We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.

Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the…

We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…

In this article we introduce the space of configurations of commuting elements in a topological group and show that it satisfies rational homological stability for the sequences of unitary, special unitary and symplectic groups. We also…

In this paper, we study some properties of self-homeomorphisms on the Mac\'ias topology over $\mathbb{N}$, and we demonstrate that this space is not topologically rigid.

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…

In this paper we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made…

If a closed orientable manifold (resp. rational Poincar\'e duality space) $X$ receives a map $Y \to X$ from a formal manifold (resp. space) $Y$ that hits a fundamental class, then $X$ is formal. The main technical ingredient in the proof…

We prove a "purity implies formality" statement in the context of the rational homotopy theory of smooth complex algebraic varieties, and apply it to complements of hypersurface arrangements. In particular, we prove that the complement of a…

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…

Compact symmetric spaces are probably one of the most prominent class of formal spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational cohomology algebra. As a generalisation, it is even known that…