Questions tagged [simple-homotopy-theory]

Any two isomorphic simplicial complexes are simple-homotopy-equivalent. This is a fairly simple result, but it is not obvious. Yet I have been surprisingly unable to find it in the literature on ...

I recently started reading up on simple homotopy theory. Here is a question I stumbled upon. In his 1938 Paper Simplicial Spaces, Nuclei and m-Groups Whitehead introduced the notion of elementary ...

Let $f : X \to Y$ and $g : Z \to Y$ be continuous maps between finite CW complexes. If $f$ is a simple homotopy equivalence, are there conditions on $g$ which guarantee that its pullback $f'$ is a ...

If we start with the category of finite complexes and continuous maps, and then identify two morphisms iff they are homotopic, we get the homotopy category of finite complexes, and it is trivial to ...

On page 256 of Kirby and Siebenmann one finds the following lemma (its proof an "elementary exercise", so they only give a hint): Taking $A$ to be a point and iterating this collapsing lemma, this ...