On categorical shape theory
On certain homotopy actions of general linear groups on iterated products
The -fold product of an arbitrary space usually supports only the obvious permutation action of the symmetric group . However, if is a -complete, homotopy associative, homotopy commutative -space one can define a homotopy action of on . In various cases, e.g. if multiplication by is null homotopic then we get a homotopy action of for some . After one suspension this allows one to split using idempotents of which can be lifted to . In fact all of this is possible if is an -space...
On co-H-spaces.
On compact symplectic and Kählerian solvmanifolds which are not completely solvable
We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.
On components of MANR-spaces
On constructing resolutions over the polynomial algebras.
On Davis-Januszkiewicz homotopy types I: formality and rationalisation.
On deformations of spherical isometric foldings
The behavior of special classes of isometric foldings of the Riemannian sphere under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the standard spherical isometric folding defined by .
On Fibrations and nilpotency - some remarks upon two articles by I. M. James.
On fine shape theory
On fine shape theory II
On Fox's theory of overlays
On fundamental deformation retracts and on some related notions
On -disconnected injective models
Let be a finite group. It was observed by L.S. Scull that the original definition of the equivariant minimality in the -connected case is incorrect because of an error concerning algebraic properties. In the -disconnected case the orbit category was originally replaced by the category with one object for each component of each fixed point simplicial subsets of a -simplicial set , for all subgroups . We redefine the equivariant minimality and redevelop some results on the rational homotopy...
On genera of polyhedra
We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write X ∼ Y if X p ≅ Y p for all prime p, where X p denotes the image of Xin the localized category S p. We prove that it is equivalent to the stable isomorphism X∨B 0 ≅Y∨B 0, where B 0 is the wedge of all spheres S n such that π nS(X) is infinite. We also prove that a stable isomorphism X ∨ X ≅ Y ∨ X implies a stable isomorphism X ≅ Y.
On generalizations of Borsuk's homotopy extension theorem
On generalized homology of Artin groups.
On genus and embeddings of torsion-free nilpotent groups of class two.
On Hochschild and cyclic homology of certain homogeneous spaces
On homotopical equivalence of tolerance spaces