We give an algorithm to find vertical essential tori in small Seifert fiber spaces with infinite fundamental group. This implies that there are algorithms to decide whether a 3-manifold is a Seifert fiber space.
Cite this article
Tao Li, An algorithm to find vertical tori in small Seifert fiber spaces. Comment. Math. Helv. 81 (2006), no. 4, pp. 727–753DOI 10.4171/CMH/71