Abstract
As we have mentioned earlier, recognizing irreducibility of 3-manifolds requires the existence of a recognition algorithm for the sphere S 3. Another motivation for constructing such an algorithm is the following. To the late seventies 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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© 2003 Springer-Verlag Berlin Heidelberg
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Matveev, S. (2003). Algorithmic Recognition of S 3 . In: Algorithmic Topology and Classification of 3-Manifolds. Algorithms and Computation in Mathematics, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05102-3_5
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DOI: https://doi.org/10.1007/978-3-662-05102-3_5
Publisher Name: Springer, Berlin, Heidelberg
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