Algorithmic Recognition of S3
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?
KeywordsManifold Stein Verse
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