A complete description for the set of fundamental surfaces in some 3-manifolds (Q1876421)

The set of all normal surfaces in a 3-manifold is a partial commutative monoid under addition with the minimal generating set of fundamental surfaces. The author obtains a complete geometric description for the fundamental surfaces of the following two infinite series of 3-manifolds equipped with the standard handle decomposition: lens spaces and generalized quaternion spaces. This is an English translation of the author's article published in the book [\textit{Yu. G. Reshetnyak} (ed.) et al., Proceedings of the conference `Geometry and applications' dedicated to the 70th anniversary of Prof. Victor Toponogov. Novosibirsk: Izdatel'stvo Instituta Matematiki (2001; Zbl 1004.57018)].