Related papers: Homotopy branching space and weak dihomotopy

Using the notion of short natural directed path, we introduce the homotopy branching space of a precubical set. It is unique only up to homotopy equivalence. We prove that, for any precubical set, it is homotopy equivalent to the branching…

A stratified space is a topological space together with a decomposition into strata corresponding to different types of singularities. Examples of such spaces appear everywhere in topology and geometry. The study of stratified spaces…

Higher homotopies are nowadays playing a prominent role in mathematics as well as in certain branches of theoretical physics. We recall some of the connections between the past and the present developments. Higher homotopies were isolated…

Given a strong homotopy pushout cube of spaces A, we measure how far it is from also being a homotopy pullback cube. Explicitly, letting P be the homotopy colimit of the diagram obtained from A by forgetting the initial vertex…

We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…

The paper is being withdrawn. A new submission will follow.

In this paper we take a look at compactly generated weak Hausdorff spaces equipped with an action of a compact Lie group $G$ together with their colimits and homotopy colimits. In particular, we investigate relations between (homotopy)…

There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. This paper is withdrawn by the author for more clear presentation.

One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…

This presentation is the sequel of a paper published in GETCO'00 proceedings where a research program to construct an appropriate algebraic setting for the study of deformations of higher dimensional automata was sketched. This paper…

We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various…

Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…

The primary goal of this paper is to study topological invariants in two dimensional twofold rotation and time-reversal symmetric spinful systems. In this paper, firstly we build a new homotopy invariant based on the lifting of the Wilson…

In this note, we study the delooping of spaces and maps in homotopy type theory. We show that in some cases, spaces have a unique delooping, and give a simple description of the delooping in these cases. We explain why some maps, such as…

We propose an axiomatic characterization of coarse homology theories defined on the category of bornological coarse spaces. We construct a category of motivic coarse spectra. Our focus is the classification of coarse homology theories and…

We prove affirmatively the conjecture raised by J. Mostovoy; the space of short ropes is weakly homotopy equivalent to the classifying space of the topological monoid (or category) of long knots in $\mathbb{R}^3$. We make use of techniques…

This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0511016) in a clearer way.

This paper has been withdrawn because of serious errors.