There are three well known model structures in the category of spaces - the Quillen's structure, the Strom's structure and the mixed structure.
I was wondering if there is some other nice structures. In particular, for a fixed $n\in\mathbb{N} $, is there a model structure in Top such that the weak equivalences are n-equivalences and the cofibrations are closed Hurewicz cofibrantions (or other nice cofibration)?


Obs.: By n-equivalence, I mean a continous function that induces isomorphisms between t-homotopy groups ($ t\leq n-1 $) and induces a surjective morphism between n-homotopy groups.


Is there any text about other useful model structures in Top?


Thank you



Top - Model structures
A different way of getting a model structure which captures "truncation" data was asked about [here](https://mathoverflow.net/questions/112069/a-fibrant-objects-structure-on-top/114916#114916), and I answered it. There a $\pi\_n$ weak equivalence is an isomorphism for $t\leq n$ but we make no mention of surjection in top degree (as Denis Charles Cisinski points out in his comment, this is the right notion of weak equivalence for your truncated model structure). The content of my answer was figuring out what a $\pi\_n$ fibration should be to make it a model structure. We also discussed "going to the limit" and recovering the usual Quillen model structure. And we discussed the other kind of truncations, where you have a $\pi\_t$ isomorphism for all $t>n$. There are a number of references on that answer which should help you.


