When localizing the semidirect product of two groups, the effect on the factors is made explicit. As an application in Topology, we show that the loop space of a based connected CW-complex is a P-local group, up to homotopy, if and only if π1X and the free homotopy groups [Sk-1, ΩX], k ≥ 2, are P-local.
In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.
We introduce the concept of conserved current variationally associated with locally variational invariant field equations. The invariance of the variation of the corresponding local presentation is a sufficient condition for the current beeing variationally equivalent to a global one. The case of a Chern-Simons theory is worked out and a global current is variationally associated with a Chern-Simons local Lagrangian.
We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking values in . These depend on first algebraically “delooping” the Π-algebras , using the H-space structure on X, and then trying to realize the delooped Π-algebra.
We study the (n+1)st homotopy groups and the shape groups of the (n-1)-fold reduced and unreduced suspensions of the Hawaiian earring.
We study the Lusternik-Schnirelmann category of some CW-complexes with 3 cells, built on Y = S2n Uk[i2n,i2n] e4n. In particular, we prove that an R-local space, in the sense of D. Anick, of LS-category 3 and of the homotopy type of a CW-complex with 3 R-cells, has a cup-product of length 3 in its algebra of cohomology. This result is no longer true in the framework of mild spaces.