On spaces having the homotopy type of ${\rm CW}$-complex

Compact Open Topology and Cw Homotopy Type

On the Homotopy Type and the Fundamental Crossed Complex of the Skeletal Filtration of a CW-Complex

We prove that if M is a CW-complex, then the homotopy type of the skeletal filtration of M does not depend on the cell decomposition of M up to wedge products with n-disks D, when the later are given their natural CW-decomposition with unique cells of order 0, (n − 1) and n; a result resembling J.H.C. Whitehead’s work on simple homotopy types. From the Colimit Theorem for the Fundamental Crosse...

On the étale homotopy type of Morel-Voevodsky spaces

On the Rational Homotopy Type of Function Spaces

The main result of this paper is the construction of a minimal model for the function space F(X,Y ) of continuous functions from a finite type, finite dimensional space X to a finite type, nilpotent space Y in terms of minimal models for X and Y . For the component containing the constant map, π∗(F(X,Y ))⊗Q = π∗(Y ) ⊗ H−∗(X;Q) in positive dimensions. When X is formal, there is a simple formula ...

On the Second Homotopy Module of Two-dimensional Cw Complexes

Let A' be a connected 2-dimensional CW complex. This note reproves from a very simple point of view two classical theorems of H. Hopf relating the homology of the fundamental group it = irx(X) of X and the Hurewicz map on ir2(X). This point of view also allows the dual theorems to be proved. If w is a finite group, a new interpretation is given for tf,(7r; Z) (/' = 2, 3) in terms of v2(X).