Free minimal resolutions and the Betti numbers of the suspension of an -gon.
Free Quillen factorization systems.
Freudenthal-Invariante.
From cubical to globular higher categories
From fibre bundles to categories
Function spaces and Hurwitz-Radon numbers.
Function spaces and shape theories
The purpose of this paper is to provide a geometric explanation of strong shape theory and to give a fairly simple way of introducing the strong shape category formally. Generally speaking, it is useful to introduce a shape theory as a localization at some class of “equivalences”. We follow this principle and we extend the standard shape category Sh(HoTop) to Sh(pro-HoTop) by localizing pro-HoTop at shape equivalences. Similarly, we extend the strong shape category of Edwards-Hastings to sSh(pro-Top)...
Functors between homotopy theories
Fundamental Groups, ...-groups and Codimension two Submanifolds
Fundamental Groups of Homogeneous Space Forms.
Fundamental groups of one-dimensional spaces
Let X be a metrizable one-dimensional continuum. We describe the fundamental group of X as a subgroup of its Čech homotopy group. In particular, the elements of the Čech homotopy group are represented by sequences of words. Among these sequences the elements of the fundamental group are characterized by a simple stabilization condition. This description of the fundamental group is used to give a new algebro-combinatorial proof of a result due to Eda on continuity properties of homomorphisms from...
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX,...
Fundamental vector fields on associated fiber bundles
Further remarks on systems of interlocking exact sequences.