ﻻ يوجد ملخص باللغة العربية
A panel structure on a topological space is just a locally finite family of closed subspaces. A space together with a panel structure is called a space with faces. In this paper, we define the notion of polyhedral product over a space with faces. This notion provides a unifying viewpoint on the constructions of polyhedral products and generalized moment-angle complexes in various settings. We compute the stable decomposition of these spaces and use it to study their cohomology ring structures by the partial diagonal maps. Besides, we can compute the equivariant cohomology ring of the moment-angle complex over a space with faces with respect to the canonical torus action. The calculation leads to a notion of topological face ring of a space with faces, which generalizes the classical notion of face ring of a simplicial complex. We will see that many known results in the study of polyhedral products and moment-angle complexes can be reinterpreted from our general theorems on the polyhedral product over a space with faces. Moreover, we can derive some new results via our approach in some settings.
Polyhedral products were defined by Bahri, Bendersky, Cohen and Gitler, to be spaces obtained as unions of certain product spaces indexed by the simplices of an abstract simplicial complex. In this paper we give a very general homotopy theoretic cons
A generalised Postnikov tower for a space $X$ is a tower of principal fibrations with fibres generalised Eilenberg-MacLane spaces, whose inverse limit is weakly homotopy equivalent to $X$. In this paper we give a characterisation of a polyhedral prod
The construction of a simplicial complex given by polyhedral joins (introduced by Anton Ayzenberg), generalizes Bahri, Bendersky, Cohen and Gitlers $J$-construction and simplicial wedge construction. This article gives a cohomological decomposition o
We show that the tensor product of two cyclic $A_infty$-algebras is, in general, not a cyclic $A_infty$-algebra, but an $A_infty$-algebra with homotopy inner product. More precisely, we construct an explicit combinatorial diagonal on the pairahedra,
We selected a sample of 33 Gamma Ray Bursts (GRBs) detected by Swift, with known redshift and optical extinction at the host frame. For these, we constructed the de-absorbed and K-corrected X-ray and optical rest frame light curves. These are modelle