On manifolds with finitely generated homotopy groups.
On minimal models in integral homotopy theory.
On spaces of the same strong -type.
On the 2-type of an iterated loop space.
On the connection between the topological genus of certain polyhedra and the algebraic genus of their Hilton-Hopt quadratic forms.
The Hilton-Hopf quadratic form is defined for spaces of the homotopy type of a CW complex with one cell each in dimensions 0 and 4n, K cells in dimension 2n and no other cells. If two such spaces are of the same topological genus, then their Hilton-Hopf quadratic forms are of the same weak algebraic genus. For large classes of spaces, such as simply connected differentiable 4-manifolds, the converse is also true, as long as the suspensions of the spaces are also of the same topological genus. This...
On the Construction of Harmonie and Holomorphic Maps Between Surfaces.
On the division by the circle
On the essential height of homotopy trees with finite fundamental group
On the foundations of Topology
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 of Non-Nilpotent Spaces.
On the homotopy of the complement to plane algebraic curves.
On the Homotopy Type of Classifying Spaces.
On the locally finite chain algebra of a proper homotopy type.
On the Space of Maps of a Closed Surface into the 2-Sphere.
On the structure of 5-dimensional Poincaré duality spaces.
On weak homotopy
Order complex of ideals in a commutative ring with identity
Order complex is an important object associated to a partially ordered set. Following a suggestion from V. A. Vassiliev (1994), we investigate an order complex associated to the partially ordered set of nontrivial ideals in a commutative ring with identity. We determine the homotopy type of the geometric realization for the order complex associated to a general commutative ring with identity. We show that this complex is contractible except for semilocal rings with trivial Jacobson radical when...
Partial homotopy type of finite two-complexes.
Polyhedra with finite fundamental group dominate finitely many different homotopy types
In 1968 K. Borsuk asked: Does every polyhedron dominate only finitely many different shapes? In this question the notion of shape can be replaced by the notion of homotopy type. We showed earlier that the answer to the Borsuk question is no. However, in a previous paper we proved that every simply connected polyhedron dominates only finitely many different homotopy types (equivalently, shapes). Here we prove that the same is true for polyhedra with finite fundamental group.