On the Euler Characteristic of Finite Unions of Convex Sets.
On the Euler characteristic of multiple selfintersection points of immersed manifolds.
On the Euler characteristic of the link of a weighted homogeneous mapping
The paper is concerned with an effective formula for the Euler characteristic of the link of a weighted homogeneous mapping with an isolated singularity. The formula is based on Szafraniec’s method for calculating the Euler characteristic of a real algebraic manifold (as the signature of an appropriate bilinear form). It is shown by examples that in the case of a weighted homogeneous mapping it is possible to make the computer calculations of the Euler characteristics much more effective.
On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes
Necessary and sufficient conditions for the existence of two linearly independent sections in an 8-dimensional spin vector bundle over a CW-complex of the same dimension are given in terms of characteristic classes and a certain secondary cohomology operation. In some cases this operation is computed.
On the existence of universal covering spaces for metric spaces and subsets of the Euclidean plane
We prove several results concerning the existence of universal covering spaces for separable metric spaces. To begin, we define several homotopy-theoretic conditions which we then prove are equivalent to the existence of a universal covering space. We use these equivalences to prove that every connected, locally path connected separable metric space whose fundamental group is a free group admits a universal covering space. As an application of these results, we prove the main result of this article,...
On the exponent of the cokernel of the forget-control map on K₀-groups
For groups that satisfy the Isomorphism Conjecture in lower K-theory, we show that the cokernel of the forget-control K₀-groups is composed by the NK₀-groups of the finite subgroups. Using this information, we can calculate the exponent of each element in the cokernel in terms of the torsion of the group.
On the Farrell cohomology of mapping class groups.
On the finiteness obstruction of certain periodic groups.
On the Finiteness Obstruction of Nilpotent Spaces of the Same Genus.
On the first homology of automorphism groups of manifolds with geometric structures
Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.
On the first secondary invariant of Molino's central sheaf
For a Riemannian foliation on a closed manifold, the first secondary invariant of Molino's central sheaf is an obstruction to tautness. Another obstruction is the class defined by the basic component of the mean curvature with respect to some metric. Both obstructions are proved to be the same up to a constant, and other geometric properties are also proved to be equivalent to tautness.
On the first two Vassiliev invariants.
On the Floer homology of plumbed three-manifolds.
On the forcing relation for surface homeomorphisms
On the form of principal torus-bundles over toruses
On the formality of products and wedges
On the four-dimensional -manifolds of positive Ricci curvature.
On the functoriality of stratified desingularizations.
On the fundamental group of a space of sections.
On the Fundamental Group of a Visibility Manifold.