Regular Genus and Products of Spheres

Abstract

Abstract. A crystallization of a closed connected PL manifold M is a special edge-colored graph representing M via a contracted triangulation. The regular genus of M is the minimum genus of a closed connected surface into which a crystallization of M regularly embeds. We disprove a conjecture on the regular genus of S 2 × S n , n ≥ 3, stated in [J. Korean Math. Soc. 41 (2004), no. 3, p. 420].