# Questions tagged [simple-homotopy-theory]

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4
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### Simplicial simple homotopy vs. cellular simple homotopy

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 ...

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### When are pullbacks of simple homotopy equivalences still simple homotopy equivalences?

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 ...

**14**

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701 views

### Is there a category whose isomorphisms are precisely the simple homotopy equivalences?

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 ...

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359 views

### A homological criterion for collapsibility?

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 ...