A Homology Transfer for a Class of Simplicial Maps.
A necessary and sufficient condition for the existence of a bundle in differential spaces
A Remark on "Homotopy Fibrations".
Abstract tangent functors
Adjunction of n-equivalences and triad connectivity.
We prove a new adjunction theorem for n-equivalences. This theorem enables us to produce a simple geometric version of proof of the triad connectivity theorem of Blakers and Massey. An important intermediate step is a study of the collapsing map S∨X → S, S being a sphere.
An introduction to shape theory for the nonspecialist
Classifying relative principal fibrations with loop space fibers
Codimension 2 fibrators that are closed under finite product.
Continuity of projections of natural bundles
This paper is a contribution to the axiomatic approach to geometric objects. A collection of a manifold M, a topological space N, a group homomorphism E: Diff(M) → Homeo(N) and a function π: N → M is called a quasi-natural bundle if (1) π ∘ E(f) = f ∘ π for every f ∈ Diff(M) and (2) if f,g ∈ Diff(M) are two diffeomorphisms such that f|U = g|U for some open subset U of M, then E(f)|π^{-1}(U) = E(g)|π^{-1}(U). We give conditions which ensure that π: N → M is continuous. In particular, if (M,N,E,π)...
Converting compact and fibrations into locally trivial bundles with compact manifolds as fibres
Decompositions into submanifolds of fixed codimension
Double vector spaces
Embedding of presheaves into dual unit balls
Fibrations and classifying spaces : overview and the classical examples
Finite spaces and the universal bundle of a group
We find sufficient conditions for a cotriad of which the objects are locally trivial fibrations, in order that the push-out be a locally trivial fibration. As an application, the universal -bundle of a finite group , and the classifying space is modeled by locally finite spaces. In particular, if is finite, then the universal -bundle is the limit of an ascending chain of finite spaces. The bundle projection is a covering projection.
Generalized universal covering spaces and the shape group
If a paracompact Hausdorff space X admits a (classical) universal covering space, then the natural homomorphism φ: π₁(X) → π̌₁(X) from the fundamental group to its first shape homotopy group is an isomorphism. We present a partial converse to this result: a path-connected topological space X admits a generalized universal covering space if φ: π₁(X) → π̌₁(X) is injective. This generalized notion of universal covering p: X̃ → X enjoys most of the usual properties, with the possible exception of evenly...
Geometric topology of stratified spaces.
Homotopy Classification of Nondegenerate Quasiperiodic Curves on the 2-sphere
Homotopy equivalences and mapping torus projections
Hopfian and strongly hopfian manifolds
Let p: M → B be a proper surjective map defined on an (n+2)-manifold such that each point-preimage is a copy of a hopfian n-manifold. Then we show that p is an approximate fibration over some dense open subset O of the mod 2 continuity set C’ and C’ ∖ O is locally finite. As an application, we show that a hopfian n-manifold N is a codimension-2 fibrator if χ(N) ≠ 0 or