On the homeomorphism problem of trivalent 2-stratifolds with finite homology groups

Trivalent 2-stratifolds X with finite homology groups can be encoded as bicolored trivalent graphs \(\Gamma \) $\mathrm{\Gamma }$ . We show that the homeomorphism problem for such stratifolds can be solved with complexity O(||V||), where V is the set of vertices of \(\Gamma \) $\mathrm{\Gamma }$ .