Rational formality of function spaces.
Rational homotopy of Serre fibrations
In rational homotopy theory, we show how the homotopy notion of pure fibration arises in a natural way. It can be proved that some fibrations, with homogeneous spaces as fibre are pure fibrations. Consequences of these results on the operation of a Lie group and the existence of Serre fibrations are given. We also examine various measures of rational triviality for a fibration and compare them with and whithout the hypothesis of pure fibration.
Rational Hopf G-spaces with two nontrivial homotopy group systems
Let G be a finite group. We prove that every rational G-connected Hopf G-space with two nontrivial homotopy group systems is G-homotopy equivalent to an infinite loop G-space.
Rational Lie Algebras and p-Isomorphisms of Nilpotent Groups and Homotopy Types.
Rational models of solvmanifolds with Kählerian structures.
We investigate the existence of symplectic non-Kählerian structures on compact solvmanifolds and prove some results which give strong necessary conditions for the existence of Kählerian structures in terms of rational homotopy theory. Our results explain known examples and generalize the Benson-Gordon theorem (Benson and Gordon (1990); our method allows us to drop the assumption of the complete solvability of G).
Rational nilpotent groups as subgroups of self-homotopy equivalences
Rational string topology
We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold . We prove that the loop homology of is isomorphic to the Hochschild cohomology of the cochain algebra with coefficients in . Some explicit computations of the loop product and the string bracket are given.
Rational toral ranks in certain algebras.
Rationale Homotopietypen.
Rationalization of Hopf G-Spaces..
Real cobordism and greek letter elements in the geometric chromatic spectral sequence.
Real Homotopy Theory of Kähler Manifolds.
Realization Problems for the Group of Homotopy Classes of Self-Equivalences.
Realizing Unstable Injectives.
Recognition of certain classes of closed maps
Reedy categories which encode the notion of category actions
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
Refinable maps in the theory of shape
Refining thick subcategory theorems
We use a K-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some commutative rings. In the stable homotopy category of spectra we obtain only...
Reflexive and dihedral (co)homology of a pre-additive category.
Regular Rational Homotopy Types.