Tetrahedra on deformed spheres and integral group cohomology.
The ℤ₂-cohomology cup-length of real flag manifolds
Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.
The Anosov theorem for infranilmanifolds with an odd-order Abelian holonomy group.
The asymptotic dimension of the first Grigorchuk group is infinity.
We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.
The boundary-Wecken classification of surfaces.
The Brouwer Fixed Point Theorem for Some Set Mappings
For some classes of closed subsets of the disc ₙ ⊂ ℝⁿ we prove that every Hausdorff-continuous mapping f: X → X has a fixed point A ∈ X in the sense that the intersection A ∩ f(A) is nonempty.
The Brouwer-Jordan theorem
The closure of a model category
The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
The coincidence index for fundamentally contractible multivalued maps with nonconvex values
We study a coincidence problem of the form A(x) ∈ ϕ (x), where A is a linear Fredholm operator with nonnegative index between Banach spaces and ϕ is a multivalued A-fundamentally contractible map (in particular, it is not necessarily compact). The main tool is a coincidence index, which becomes the well known Leray-Schauder fixed point index when A=id and ϕ is a compact singlevalued map. An application to boundary value problems for differential equations in Banach spaces is given.
The coincidence Nielsen number for maps into real projective spaces
We give an algorithm to compute the coincidence Nielsen number N(f,g), introduced in [DJ], for pairs of maps into real projective spaces.
The compact extension property: the role of compactness
We consider separable metrizable topological spaces. Among other things we prove that there exists a non-contractible space with the compact extension property and we prove a new version of realization of polytopes for ’s.
The Degree of a Map Between Surfaces.
The degrees of certain strata of the dual variety
The Equivariant Bundle Subtraction Theorem and its applications
In the theory of transformation groups, it is important to know what kind of isotropy subgroups of G do occur at points of the space upon which the given group G acts. In this article, for a finite group G, we prove the Equivariant Bundle Subtraction Theorem (Theorem 2.2) which allows us to construct smooth G-manifolds with prescribed isotropy subgroups around the G-fixed point sets. In Theorem 0.1, we restate Oliver's result about manifolds M and G-vector bundles over M that occur, respectively,...
The Fixed Point Index of Fibre-Preserving Maps.
The Fixed Point Transfer of Fibre-Preserving Maps.
The Formal Dimension of a Toplogical Space.
The homology of spaces of simple topological measures
The simple topological measures X* on a q-space X are shown to be a superextension of X. Properties inherited from superextensions to topological measures are presented. The homology groups of various subsets of X* are calculated. For a q-space X, X* is shown to be a q-space. The homology of X* when X is the annulus is calculated. The homology of X* when X is a more general genus one space is investigated. In particular, X* for the torus is shown to have a retract homeomorphic to an infinite product...
The Homotopy Category of Spectra. III.