Given a principal ideal domain of characteristic zero, containing 1/2, and a two-cone of appropriate connectedness and dimension, we present a sufficient algebraic condition, in terms of Adams-Hilton models, for the Hopf algebra to be isomorphic with the universal enveloping algebra of some -free graded Lie algebra; as usual, stands for free part, for homology, and for the Moore loop space functor.
In the rational cohomology of a 1-connected space a structure of -algebra is constructed and it is shown that this object determines the rational homotopy type.
We study cohomology algebras of graded differential algebras which are models for Hochschild homology of some classes of topological spaces (e.g. homogeneous spaces of compact Lie groups). Explicit formulae are obtained. Some applications to cyclic homology are given.
The aim of this paper is to present a starting point for proving existence of injective minimal models (cf. [8]) for some systems of complete differential graded algebras.
In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.
We prove the formality property of total spaces of fat bundles over compact homogeneous spaces. Some rational homotopy obstructions to fatness are obtained.
We review topological properties of Kähler and symplectic manifolds, and of their odd-dimensional counterparts, coKähler and cosymplectic manifolds. We focus on formality, Lefschetz property and parity of Betti numbers, also distinguishing the simply-connected case (in the Kähler/symplectic situation) and the b1 = 1 case (in the coKähler/cosymplectic situation).