A simple proof of Gagliardi's handle recognition theorem

AbstractRecently Gagliardi [2] has proved a theorem on recognizing handles in 3-manifolds crystallizations [3]. The purpose of this note is to present a short proof of this result which follows as a corollary of Theorem 2 and to introduce a more general definition of combinatorial handle, crucial for the proof. We also present a crystallization which settles two questions posed in [2]