Related papers: On loop spaces with marking

It is shown that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. Furthermore, their homotopy categories are equivalent to the homotopy categories of…

This paper is part of a series of papers about homotopy theory of strict $n$-categories. In the first paper of this series, we gave conditions that guarantee the existence of a Thomason model category structure on the category of strict…

The fundamental groupoid of a space becomes enriched over the category of topological spaces when the hom-sets are endowed with topologies intimately related to universal constructions of topological groups. This paper is devoted to a…

In this note, we show that the homotopy type of a complex manifold X satisfying the Oka property is captured by holomorphic maps from the affine spaces C^n, n\geq 0, into X. Among such X are all complex Lie groups and their homogeneous…

We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical…

The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from…

This paper aims to find the most general combinatorial conditions under which a moment-angle complex $(D^2,S^1)^K$ is a co-$H$-space, thus splitting unstably in terms of its full subcomplexes. In this way we study to which extent the…

We provide a construction for holes into which morphisms of abstract symmetric monoidal categories can be inserted, termed the polyslot construction pslot[C], and identify a sub-class srep[C] of polyslots that are single-party…

A loop is shown to be a universal Osborn loop if and only if it has a particular simplicial complex. A loop is shown to be a universal Osborn loop and obeys two new identities if and only if it has another particular simplicial complex. A…

A simplicial set is said to be non-singular if its non-degenerate simplices are embedded. Let $sSet$ denote the category of simplicial sets. We prove that the full subcategory $nsSet$ whose objects are the non-singular simplicial sets…

We exhibit a Quillen equivalence between two model categories encoding the homotopy theory of stratified spaces : the model category of filtered simplicial sets, and that of filtered spaces. Additionally, we introduce a new class of…

This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition…

We develop a notion of iterated monoidal category and show that this notion corresponds in a precise way to the notion of iterated loop space. Specifically the group completion of the nerve of such a category is an iterated loop space and…

We investigate algebraic structures that can be placed on vertices of the multiplihedra, a family of polytopes originating in the study of higher categories and homotopy theory. Most compelling among these are two distinct structures of a…

Methods are developed to relate the action of a principal fibration to relative Whitehead products in order to determine the homotopy type of certain spaces. The methods are applied to thoroughly analyze the homotopy type of the based loops…

Let $\mathbf{k}$ be the field $\mathbb{F}_p$ or the ring $\mathbb{Z}$. We study combinatorial and topological properties of the universal simplicial complexes $X(\mathbf{k}^n)$ and $K(\mathbf{k}^n)$ whose simplices are certain unimodular…

We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…

Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant…

We construct "higher" motion planners for automated systems whose space of states are homotopy equivalent to a polyhedral product space $Z(K,\{(S^{k_i},\star)\})$, e.g. robot arms with restrictions on the possible combinations of…

Let M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M,boundary of M) can be recovered from the configuration category of the interior of M. The grouplike monoid of…