2018/12/31 by Burton, Benjamin A., Tillmann, Stephan
#57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1812.11686
We present a practical algorithm to test whether a 3-manifold given by a triangulation or an ideal triangulation contains a closed essential surface. This property has important theoretical and algorithmic consequences. As a testament to its practicality, we run the algorithm over a comprehensive body of closed 3-manifolds and knot exteriors, yielding results that were not previously known. The algorithm derives from the original Jaco-Oertel framework, involves both enumeration and optimisation procedures, and combines several techniques from normal surface theory. Our methods are relevant for other difficult computational problems in 3-manifold theory, such as the recognition problem for knots, links and 3-manifolds.