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Computational topology is the study of decidability problems in topology and the algorithms that determine decidability. Examples of area of study include Normal Surface theory and the subproblems of unknot and $S^3$ recognition.
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Is there an algorithm for the genus of a knot?
There is an algorithm using normal surface theory, originally developed by Haken and Schubert to compute the genus of any knot. These articles are in German, but for a reference in English, one could …