On the Homology of Finite Free (Z/2)n-Complexes.
On the homology of mapping spaces
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.
On the Homology of Non-Connected Monoids and Their Associated Groups
On the homology of small categories and asynchronous transition systems.
On the homology of the Harmonic Archipelago
We calculate the singular homology and Čech cohomology groups of the Harmonic Archipelago. As a corollary, we prove that this space is not homotopy equivalent to the Griffiths space. This is interesting in view of Eda’s proof that the first singular homology groups of these spaces are isomorphic.
On the homology of the special linear group ove a number field.
On the Homology Structure of Submersions.
On the homology theory of discrete spaces
On the homotopical classification of DJ-mappings of infnitely dimensional spheres
On the homotopy category of Moore spaces and the cohomology of the category of abelian groups
The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.
On the homotopy embeddability of complexes in Euclidean space. I. The weak thickening theorem.
On the homotopy equivalence of the spaces of proper and local maps
We prove that for n > 1 the space of proper maps P 0(n, k) and the space of local maps F 0(n, k) are not homotopy equivalent.
On the homotopy groups of a finite dimensional space.
On the homotopy invariance of configuration spaces.
On the homotopy inverse limits of transfer maps.
On the Homotopy of Non-Nilpotent Spaces.
On the homotopy of the complement to plane algebraic curves.
On the Homotopy Properties of Thom Complexes.
On the homotopy transfer of structures
The present article is devoted to the study of transfers for structures, their maps and homotopies, as developed in [7]. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.
On the homotopy type of a chain algebra.