Concerning a problem due to Sam B. Nadler, Jr.
Concerning the shape groups of compact metric spaces
Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group
We prove that Alexander-Spanier cohomology with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.
Continuously factorable groupoids.
Cutting description of trivial 1-cohomology
A characterisation of trivial 1-cohomology, in terms of some connectedness condition, is presented for a broad class of metric spaces.
Foundations of Vietoris homology theory with applications to non-compact spaces [Book]
Homology with equationally compact coefficients
Homology with models
Idempotent Topological Groupoids with Non-Empty Center.
Local Formulae for Stiefel-Whitney classes.
Localization of Topological Pontryagin Classes via Finite Propagation Speed.
Mappings onto circle-like continua
Maps between Classifying Spaces.
Maximal equicontinuous factors and cohomology for tiling spaces
We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that in degree one this map is injective and has torsion free cokernel. We show by example, however, that, in degree one, the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology.
Non-standard analysis and homology
On Čech cohomology and weakly confluent mappings into ANR's
On certain homological properties of finite-dimensional compacta. Carriers, minimal carriers and bubbles
On -bubbles in n-dimensional compacta
A topological space X is called an -bubble (n is a natural number, is Čech cohomology with integer coefficients) if its n-dimensional cohomology is nontrivial and the n-dimensional cohomology of every proper subspace is trivial. The main results of our paper are: (1) Any compact metrizable -bubble is locally connected; (2) There exists a 2-dimensional 2-acyclic compact metrizable ANR which does not contain any -bubbles; and (3) Every n-acyclic finite-dimensional -trivial metrizable compactum...
On shape groups and Cech homology groups of a compact space
On shapes of topological spaces