Journal of the
Korean Mathematical Society JKMS

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 $\mathbb S^2 \times \mathbb S^n$, $n\ge 3$, stated in [J. Korean Math. Soc. $\boldsymbol{41}$ (2004), no. 3, p. 420].

Keywords: PL manifold, regular genus, product of spheres, crystallization

MSC numbers: 57M15, 57Q15, 05C10