Related papers: The cone length and category of maps: pushouts, pr…

We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational…

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…

James' sectional category and Farber's topological complexity are studied in a general and unified framework. We introduce `relative' and `strong relative' forms of the category for a map. We show that both can differ from sectional…

A new type of Hopf invariant is described for the fiber of the pinch map from the mapping cone of a map from A to X onto to the suspension of A; this is then used to study the boundary map in the fibration sequence of Cohen, Moore and…

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…

We analyze a general family of fibrations which, after looping, have sections. Methods are developed to determine the homotopy type of the fibre and the homotopy classes of the map from the fibre to the base. The methods are driven by…

We study a generalization of the Svarc genus of a fiber map. For an arbitrary collection E of spaces and a map f:X-->Y, we define a numerical invariant, the E-sectional category of f, in terms of open covers of Y. We obtain several basic…

The homotopy theory of higher categorical structures has become a relevant part of the machinery of algebraic topology and algebraic K-theory, and this paper contains contributions to the study of the relationship between B\'enabou's…

Lusternik-Schnirelmann category (LS-category) of a topological space is the least integer $n$ such that there is a covering of $X$ by $n+1$ open sets, each of them being contractible in $X$. The cone length is the minimum number of…

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to…

The inclusion of 1-categories into $(\infty,1)$-categories fails to preserve colimits in general, and pushouts in particular. In this note, we observe that if one functor in a span of categories belongs to a certain previously-identified…

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…

In this paper we study the reduced and unreduced $L^{q,p}$-cohomology groups of manifolds of bounded geometry and their behavior under uniform maps. A \textit{uniform map} is a uniformly continuous map such that the diameter of the preimage…

Under certain conditions, we describe the homotopy type of the homo-topy fibre of the inclusion map F\_n(X) $\rightarrow$ $\prod$\_1^n X for the n-th configuration space F\_n(X) of a topological manifold X without boundary such that dim(X)…

If $q:Y\longrightarrow{B}$ is a fibration and $Z$ is a space, then the free range mapping space $Y!Z$ has a collection of partial maps from $Y$ to $Z$ as underline space, i.e. those such maps whose domains are individual fibre of $q$. It is…

Let $I=[0,1]$ and consider disjoint closed regions $G_{1},....,G_{n}$ in $% I\times I$ and subintervals $I_{1},......,I_{n},$ such that $G_{i}$ projects onto $I_{i.}$ We define the lower and upper maps $\tau_{1},$ $\tau_{2}$ by the lower…

We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. The…

A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…

We gather conditions on a class H of continuous maps of topological spaces that allow a reasonable theory of fibrations up to an equivalence (a map from this class) which we call H-fibrations. The weak homotopy equivalences recover…

We give a construction of an L-infinity map from any L-infinity algebra into its truncated Chevalley-Eilenberg complex as well as its cyclic and A-infinity analogues. This map fits with the inclusion into the full Chevalley-Eilenberg…