Related papers: Loop spaces of polyhedral products associated with…
A simplicial complement P is a sequence of subsets of [m] and the simplicial complement P corresponds to a unique simplicial complex K with vertices in [m]. In this paper, we defined the homology of a simplicial complement…
We show that the loop homology algebras of polyhedral products of the form $(\underline{X},\underline{*})^{\mathcal{K}}$ can be written as a colimit over the flagification of $\mathcal{K}$, and obtain a similar result for the Poincar\'e…
We show that the complex of free factors of a free group of rank n > 1 is homotopy equivalent to a wedge of spheres of dimension n-2. We also prove that for n > 1, the complement of (unreduced) Outer space in the free splitting complex is…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…
We present a definition of homotopy algebra for an operad, and explore its consequences. The paper should be accessible to topologists, category theorists, and anyone acquainted with operads. After a review of operads and monoidal…
We show that Lupercio-Uribe-Xicot\'{e}ncatl's orbifold loop product and coproduct can be described by a group cohomology class in some cases. By computing this cohomology class, we show that in some cases the orbifold loop product is…
We introduce a common domain of definition for the loop product and the loop coproduct, reduced loop homology, on which they combine to a unital infinitesimal anti-symmetric bialgebra structure. In particular, a relation conjectured by…
We consider the problem of describing the Pontryagin algebra (loop homology) of moment-angle complexes and manifolds. The moment-angle complex Z_K is a cell complex built of products of polydiscs and tori parametrised by simplices in a…
A well-known construction of associahedra comes from truncations of simplices. Motivated by compactifications of point configurations, we show associahedra as truncations of certain products of simplices. This is then used to provide a…
Let M be one of the projective spaces CP^n, HP^n for n>1 or the Cayley projective plane OP^2, and let LM denote the free loop space on M. Using Morse theory methods, we prove that the suspension spectrum of (LM)_+ is homotopy equivalent to…
This paper is a sequel to [Caine A., Pickrell D., arXiv:0710.4484], where we studied the Hamiltonian systems which arise from the Evens-Lu construction of homogeneous Poisson structures on both compact and noncompact type symmetric spaces.…
We show how a certain type of CW simplicial resolutions of space by wedges of spheres may be constructed for any topological space, and how such resolutions yield an obstruction theory for a given space X to be a loop space.
The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres…
In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and…
We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian…
Hyperoctahedral homology for involutive algebras is the homology theory associated to the hyperoctahedral crossed simplicial group. It is related to equivariant stable homotopy theory via the homology of equivariant infinite loop spaces. In…
`Loop-fusion cohomology' is defined on the continuous loop space of a manifold in terms of \vCech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that…
We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum, after looping. This takes inspiration from recent work of Jeffrey…
We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for…