As we have mentioned earlier, recognizing irreducibility of 3-manifolds requires the existence of a recognition algorithm for the sphere S3. Another motivation for constructing such an algorithm is the following. To the late 1970s topologists elaborated methods for proving an algorithmic classification theorem for Haken manifolds (though a complete proof appeared only in 1997, see Chap. 6). These methods play a crucial role in solving many other problems about Haken manifolds, but they do not work for manifolds which are not sufficiently large. What can one do with them?
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© 2007 Springer-Verlag Berlin Heidelberg
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(2007). Algorithmic Recognition of S3. In: Algorithmic Topology and Classification of 3-Manifolds. Algorithms and Computation in Mathematics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45899-9_5
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DOI: https://doi.org/10.1007/978-3-540-45899-9_5
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