Thank you very much. If I get it right a 2-polyhedron is in fact just a 2 dimensional simplicial complex and collapsing this 2-polyhedron $K$ with $K \times I$ means in fact that it is "expanded" to a 3 dimensional object and then collapses to a point?

Of course, these connections between Matroids and other subjects are fascinating. For example, i once conjectured a link between knot theory and matroids where you realize knots as polygonal circuits

thanks for that post, but I searched evidence not particular from AC-Conjecture but more from thoughts about collapsibilty