A Converse to the P.A. Smith Theorem for Nonunitary Homology Spheres.
A counterexample concerning products in the shape category
We exhibit a metric continuum X and a polyhedron P such that the Cartesian product X × P fails to be the product of X and P in the shape category of topological spaces.
A Counterexample to a Conjecture of Steenrod.
A counterexample to a group completion conjecture of J. C. Moore.
A counterexample to the smoothness of the solution to an equation arising in fluid mechanics
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...
A criterion of SNT(X) = {[X]} for hyperformal spaces
We will give a condition characterizing spaces X with SNT(X) = {[X]} which generalizes the corresponding result of McGibbon and Moller [8] for rational H-spaces.
A de Rham theorem in the context of noncommutative geometry.
A Decomposability Criterion for Algebraic 2-Bundles on Projective Spaces.
A Decomposition Theorem for the Integral Homology of a Variety.
A Definition of Exotic Characteristic Classes of Spherical Fibrations
A degree for a class of acyclic-valued vector fields in Banach spaces
A degree theory for almost continuous functions
A dimensional property of Cartesian product
We show that the Cartesian product of three hereditarily infinite-dimensional compact metric spaces is never hereditarily infinite-dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.
A double complex related with a system of partial differential equations. II
A double complex related with a system of partial differential equations. I
A Drived Homotopy Product.
A duality on simplicial complexes.
A Duality Theorem for Complex Manifolds.
-algebras and topology of mapping tori
The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.
A Fiber bundle theorem.