Every 3-dimensional manifold has a triangulation. But recognising a manifold from its triangulation is a tough problem. I will talk about the computational complexity of this problem and about techniques to relate triangulations which have special properties.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/TopologySeminar