Homotopy equivalences of punctured manifolds.

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...

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...

Equivariant Homotopy Epimorphisms, Homotopy Monomorphisms and Homotopy Equivalences

Configuration Spaces on Punctured Manifolds

The object here is to study the following question in the homotopy theory of configuration spaces of a general manifold M : When is the fibration Fk+1(M) → Fr(M), r < k + 1, fiber homotopically trivial? The answer to this question for the special cases when M is a sphere or euclidean space is given in [4]. The key to the solution of the problem for compact manifolds M is the study of an associa...