Smooth Compact Lie Group Actions on Disks.
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...
Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.