Lax operad actions and coherence for monoidal -categories, rings and modules.
LVM and LVMB manifolds are a large family of non kähler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a natural action of a real torus and the quotient of this action is a polytope. This quotient allows us to relate closely LVM manifolds to the moment-angle manifolds studied by Buchstaber and Panov. Our aim is to generalize the polytope associated to a LVM manifold to the LVMB case and study the properties of this generalization....
In many situations, minimal models are used as representatives of homotopy types. In this paper we state this fact as an equivalence of categories. This equivalence follows from an axiomatic definition of minimal objects. We see that this definition includes examples such as minimal resolutions of Eilenberg-Nakayama-Tate, minimal fiber spaces of Kan and Λ-minimal Λ-extensions of Halperin. For the first one, this is done by generalizing the construction of minimal resolutions of modules to complexes....
The paper is devoted to the study of the space of multiplicative maps from the Eilenberg-MacLane spectrum Hℤ to an arbitrary ring spectrum R. We try to generalize the approach of Schwede [Geom. Topol. 8 (2004)], where the case of a very special R was studied. In particular we propose a definition of a formal group law in any ring spectrum, which might be of independent interest.
Taking cylinder objects, as defined in a model category, we consider a cylinder construction in a cofibration category, which provides a reformulation of relative homotopy in the sense of Baues. Although this cylinder is not a functor we show that it verifies a list of properties which are very closed to those of an I-category (or category with a natural cylinder functor). Considering these new properties, we also give an alternative description of Baues’ relative homotopy groupoids.
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...