Tsutsumi, Yukihiro An algorithm for acylindrical surfaces in 3-manifolds. (English) Zbl 1009.57026 Tokyo J. Math. 24, No. 2, 395-405 (2001). The author presents an algorithm to decide if an orientable atoroidal 3-manifold contains closed incompressible acylindrical surfaces and to construct them if they exist. The algorithm uses normal surface theory. To prove that the algorithm stops after a finite number of steps, the author shows that each acylindrical surface is isotopic to an edge surface. Reviewer: James Hebda (St.Louis) Cited in 1 Document MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57M99 General low-dimensional topology Keywords:3-manifolds; incompressible surfaces; edge surfaces; normal surface theory; algorithm PDFBibTeX XMLCite \textit{Y. Tsutsumi}, Tokyo J. Math. 24, No. 2, 395--405 (2001; Zbl 1009.57026) Full Text: DOI