Related papers: Loop spaces of polyhedral products associated with…
The question of whether a given H-space X is, up to homotopy, a loop space has been studied from a variety of viewpoints. Here we address this question from the aspect of homotopy operations, in the classical sense of operations on homotopy…
For dimensions n greater than or equal to 3, we show that the space of metrics of positive scalar curvature on the n-sphere is homotopy equivalent to a subspace which takes the form of a H-space with a homotopy commutative, homotopy…
We show that if the moment-angle complex $\mathcal{Z}_K$ associated to a simplicial complex $K$ is homotopy equivalent to a connected sum of sphere products with two spheres in each product, then $K$ decomposes as the simplicial join of an…
We show that a moment-angle manifold associated to a neighbourly triangulation of an odd dimensional sphere is homotopy equivalent to a connected sum of products of two spheres, resolving a problem of Buchstaber and Panov. The methods are…
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 introduce a notion of polyhedral product over a space with…
In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into…
We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…
We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of…
We give p-local homotopy decompositions of the loop spaces of compact, simply-connected symmetric spaces for quasi-regular primes. The factors are spheres, sphere bundles over spheres, and their loop spaces. As an application, upper bounds…
We prove that certain conditions on multigraded Betti numbers of a simplicial complex $K$ imply existence of a higher Massey product in cohomology of a moment-angle-complex $\mathcal Z_K$, which contains a unique element (a strictly defined…
A characterization of simplicial objects in categories with finite products obtained by the reduced bar construction is given. The condition that characterizes such simplicial objects is a strictification of Segal's condition guaranteeing…
Any finite simplicial complex K and a partition of the vertex set of K determines a canonical quotient space of the moment-angle complex of K. We prove that the cohomology groups of such a space can be computed via some Hochster's type…
We show that the Hurewicz image in the homology of a moment-angle complex, when passed through an isomorphism with the Ext-module of the corresponding Stanley-Reisner ideal, contains the linear strand of this ideal. This recovers and…
In this paper, we compute the cohomology ring of all homology split polyhedral product spaces and the cohomology algebra over a field of all polyhedral product spaces. As an application, we give two polyhedral product spaces such that all…
Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the…
Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an…
In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral join complexes. Then we compute the universal algebra of polyhedral join complexes under certain split conditions and…
We determine loop space decompositions of simply-connected four-manifolds, $(n-1)$-connected $2n$-dimensional manifolds provided $n\notin\{4,8\}$, and connected sums of products of two spheres. These are obtained as special cases of a more…
For a finite simplicial complex K and a CW-pair (X,A), there is an associated CW-complex Z_K(X,A), known as a polyhedral product. We apply discrete Morse theory to a particular CW-structure on the n-sphere moment-angle complexes Z_K(D^{n},…
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…