Abstract
It is our goal to determine whether a given multibranched surface can be embedded in the 3-sphere or not.
In a similar way to the forbidden graph characterization in Graph Theory, we define a minor for multibranched surfaces and consider the forbidden minor.
On the other hand, we define a critical 2-complex.
It turns out that any forbidden multibranched surface contains a critical 2-complex.
In this talk, we exhibit forbidden minor multibranched surfaces which are $K_5 \times S^1$ and $K_{3,3} \times S^1$ families and critical 2-complexes which are contained in that.
This is a joint work with Mario Eudave-Muñoz.
