Self-homotopy equivalences of $H_*(-;\bold Z/p)$-local spaces

Self-Homotopy Equivalences of Product Spaces

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...

Selt homotopy equivalences of virtually nilpotent spaces *

The aim of this paper is to prove Theorem 1.1 below, a generalization to virtually nilpotent spaces of a result of Wilkerson [13] and Sullivan [12]. We recall that a CW complex Y is virtually nilpotent if (i) Y is connected, (ii) 7r~ Y is virtually nilpotent (i.e. has a nilpotent subgroup of finite index) and (iii) for every integer n > 1, zr~Y has a subgroup of finite index which acts nilpoten...

Leafwise Homotopy Equivalences and Leafwise Sobolov Spaces

We prove that a leafwise homotopy equivalence between compact foliated manifolds induces a well defined bounded operator between all Sobolov spaces of leafwise (for the natural foliations of the graphs of the original foliations) differential forms with coefficients in a leafwise flat bundle. We further prove that the associated map on the leafwise reduced L2 cohomology is an isomorphism which ...

Self Homotopy Equivalences of Classifying Spaces of Compact Connected Lie Groups

In an earlier paper [JMO], we gave a complete description of all homotopy classes of self maps of the classifying space BG, when G is any compact connected simple Lie group. In this paper, we extend those results to the case where G is any compact connected Lie group, but only considering self maps of BG which are rational equivalences. Most of the paper deals with self maps of the p-adic compl...