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, 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

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