ar X iv : 0 70 5 . 41 66 v 2 [ m at h . G T ] 1 2 Ju n 20 07 CLASSIFICATION OF FRAMED LINKS IN 3 - MANIFOLDS
نویسنده
چکیده
We present a short complete proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: Let M be a connected oriented closed smooth 3-manifold, L1(M) be the set of framed links in M up to a framed cobordism, and deg : L1(M) → H1(M ;Z) be the map taking a framed link to its homology class. Then for each α ∈ H1(M ;Z) there is a 1-1 correspondence between the set deg α and the group Z2d(α), where d(α) is the divisibility of the projection of α to the free part of H1(M ;Z).
منابع مشابه
ar X iv : 0 70 5 . 41 66 v 1 [ m at h . G T ] 2 9 M ay 2 00 7 CLASSIFICATION OF FRAMED LINKS IN 3 - MANIFOLDS
We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: Theorem. Let M be a connected oriented closed smooth 3-manifold. Let L1(M) be the set of framed links in M up to a framed cobordism. Let deg : L1(M) → H1(M ;Z) be the map taking a framed link to its homology class. Then for each α ∈ H1(M ;Z) there is a 1-1 ...
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تاریخ انتشار 2008