Haken is one of the first topologists who realized that the right strategy to investigate 3-manifolds is to look over the set of surfaces that are contained in them. It turned out that this infinite set has an algorithmically constructible finite basis, and thus admits an explicit description. The main idea of Haken’s method consists in decomposing a given manifold M into simple pieces and considering how the surfaces intersect the pieces.
The course will study three-dimensional topology algorithms based on the Haken’s method. Such algorithms, in particular, include a three-dimensional sphere recognition algorithm and a trivial knot recognition algorithm.