Constructing homotopy equivalences

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...

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy 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...

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 ...