Rational homotopy nilpotency of self-equivalences

Reducibility of Self-homotopy Equivalences

We describe a new general method for the computation of the group Aut(X) of self-homotopy equivalences of a space. It is based on the decomposition of Aut(X) induced by a factorization of X into a product of simpler spaces. Normally, such decompositions require assumptions (’induced equivalence property’, ’diagonalizability’), which are strongly restrictive and hard to check. In this paper we d...

Self-Homotopy Equivalences of Product Spaces

Determination of the multiplicative nilpotency of self-homotopy sets

The semigroup of the homotopy classes of the self-homotopy maps of a finite complex which induce the trivial homomorphism on homotopy groups is nilpotent. We determine the nilpotency of these semigroups of compact Lie groups and finite Hopf spaces of rank 2. We also study the nilpotency of semigroups for Lie groups of higher rank. Especially, we give Lie groups with the nilpotency of the semigr...

Coglueing Homotopy Equivalences

in which the front square is a pull-back. Then P is often called the fibre-product o f f and p, and it is also said that ~: P ~ X is induced by f from p. The map ~: Q~ P is determined by ~01 and q)2. Our object is to give conditions on the front and back squares which ensure that if q~l, q~2 and ~o are homotopy equivalences, then so also is ~. First of all we shall assume throughout that the ba...

On stable homotopy equivalences

A fundamental construction in the study of stable homotopy is the free infinite loop space generated by a space X. This is the colimit QX = lim −→ ΩΣX. The i homotopy group of QX is canonically isomorphic to the i stable homotopy group of X. Thus, one may obtain stable information about X by obtaining topological results about QX. One such result is the Kahn-Priddy theorem [7]. In another direc...