اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe efficient certification of knottedness and Thurston norm
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تأليف
Marc Lackenby
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We show that the problem of determining whether a knot in the 3-sphere is non-trivial lies in NP. This is a consequence of the following more general result. The problem of determining whether the Thurston norm of a second homology class in a compact orientable 3-manifold is equal to a given integer is in NP. As a corollary, the problem of determining the genus of a knot in the 3-sphere is in NP. We also show that the problem of determining whether a compact orientable 3-manifold has incompressible boundary is in NP.
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We present an overview of the study of the Thurston norm, introduced by W. P. Thurston in the seminal paper A norm for the homology of 3-manifolds (written in 1976 and published in 1986). We first review fundamental properties of the Thurston norm of
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