Related papers: Directed homotopy modules

In this paper we present the notion of smooth CW complexes given by attaching cubes on the category of diffeological spaces, and we study their smooth homotopy structures related to the homotopy extension property.

We give a new construction of the holonomy groupoid of a regular foliation in terms of a partial connection on a diffeological principal bundle of germs of transverse parametrisations. We extend these ideas to construct a novel holonomy…

In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid $\wEnd\vec{P}_n$ of all weak endomorphisms of a directed path with $n$ vertices, which…

We describe a homotopy-theoretic approach to the theory of moduli of realizations of Blanc-Dwyer-Goerss, reproducing their obstructions to realizing a given $\Pi$-algebra as homotopy groups of a pointed space. Our techniques are based on…

This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…

This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.

By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…

In a previous paper [22] the author studied the directed weak covering homotopy property (dWCHP)and directed weak fibrations in the category dTop of directed spaces in the sense of M. Grandis [12], [13], [14]. This type of maps extend to…

This paper studies a notion of directed homology for preordered spaces, called the homology digraph. We show that the homology digraph is a directed homotopy invariant and establish variants of the main results of ordinary singular homology…

This paper constructs model structures on the categories of coalgebras and pointed irreducible coalgebras over an operad. The underlying chain-complex is assumed to be unbounded and the results for bounded coalgebras over an operad are…

The aim of this work is to clarify the relationship between homology theory of commutative monoids constructed 'a la Quillen and technology of Gamma-modules.

We study the homology of pointed sets over a partially commutative monoid.

Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is monotonic with respect to the new ordering.…

We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…

A simple construction of Whitham type hierarchies in all genera is suggested. Potentials of these hierarchies are written as integrals of hypergeometric type. Possible generalization for universal moduli space is also briefly discussed.

For a pointed topological space $X$, we use an inductive construction of a simplicial resolution of $X$ by wedges of spheres to construct a "higher homotopy structure" for $X$ (in terms of chain complexes of spaces). This structure is then…

We interpret divided power structures on the homotopy groups of simplicial commutative rings as having a counterpart in divided power structures on chain complexes coming from a non-standard symmetric monoidal structure.

Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the…

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…

Let $M$ be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of $\Sigma M$ in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate…