Smith theory for algebraic varieties.
Our aim is to show a method of finding all natural transformations of a functor into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps commuting with -soldered automorphisms of a double vector space are investigated. On the set of such mappings, appropriate partial operations are introduced. The natural transformations are bijectively related with the elements...
Let E be the total space of a Hurewicz fiber space whose base and all fibers are ANRs. We prove that if E is metrisable, then it is also an ANR.
One wonders or not whether it is possible to determine the homotopy class of a vector field by examining some algebraic invariants associated with its qualitative behavior. In this paper, we investigate the algebraic invariants which are usually associated with the periodic solutions of non-singular Morse-Smale vector fields on the 3-sphere. We exhibit some examples for which there appears to be no correlation between the algebraic invariants of the periodic solutions and the homotopy classes of...