## Tokyo Journal of Mathematics

### An Algorithm for Acylindrical Surfaces in 3-manifolds

Yukihiro TSUTSUMI

#### Abstract

An algorithm to decide if an orientable atoroidal 3-manifold contains closed incompressible acylindrical surfaces, and construct closed incompressible acylindrical surfaces is given. Mainly, the normal surface theory is used. To assure that the algorithm stops after finite steps, we show that each acylindrical surface is isotopic to some edge surface'' which is constructible.

#### Article information

Source
Tokyo J. Math., Volume 24, Number 2 (2001), 395-405.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.tjm/1255958183

Digital Object Identifier
doi:10.3836/tjm/1255958183

Mathematical Reviews number (MathSciNet)
MR1874979

Zentralblatt MATH identifier
1009.57026

#### Citation

TSUTSUMI, Yukihiro. An Algorithm for Acylindrical Surfaces in 3-manifolds. Tokyo J. Math. 24 (2001), no. 2, 395--405. doi:10.3836/tjm/1255958183. https://projecteuclid.org/euclid.tjm/1255958183