un 2 00 2 FRAMED AND ORIENTED LINKS OF CODIMENSION 2
نویسنده
چکیده
Sanderson [12] gave an isomorphism θ : πm(∨ r i=1S 2 i ) −→ πm(∨ r+1 i=1 CP∞ i ). In this paper we construct for any subset σ ⊂ {1, 2, · · · , r} an isomorphism θσ from πm(∨ r i=1S 2 i ) to πm(∨ r+1 i=1 CP∞ i ). The inclusion S ∨ S →֒ CP∞ ∨ CP∞ induces a homomorphism f : πm(S 2 ∨ S) −→ πm(CP ∞ ∨ CP∞). We also compute f by evaluating f on each factor in the Hilton splitting of πm(S 2 ∨ S), the results in [12] concerning the case m = 4 are generalized.
منابع مشابه
ar X iv : m at h / 02 05 30 0 v 2 [ m at h . G T ] 1 J un 2 00 2 FRAMED AND ORIENTED LINKS OF CODIMENSION 2
Sanderson [12] gave an isomorphism θ : πm(∨ r i=1S 2 i ) −→ πm(∨ r+1 i=1 CP∞ i ). In this paper we construct for any subset σ ⊂ {1, 2, · · · , r} an isomorphism θσ from πm(∨ r i=1S 2 i ) to πm(∨ r+1 i=1 CP∞ i ). The inclusion S ∨ S →֒ CP∞ ∨ CP∞ induces a homomorphism f : πm(S 2 ∨ S) −→ πm(CP ∞ ∨ CP∞). We also compute f by evaluating f on each factor in the Hilton splitting of πm(S 2 ∨ S).
متن کامل2 8 M ay 2 00 2 FRAMED AND ORIENTED LINKS OF CODIMENSION 2
Sanderson [12] gave an isomorphism θ : πm(∨ r i=1S 2 i ) −→ πm(∨ r+1 i=1 CP∞ i ). In this paper we construct for any subset σ ⊂ {1, 2, · · · , r} an isomorphism θσ from πm(∨ r i=1S 2 i ) to πm(∨ r+1 i=1 CP∞ i ). The inclusion S ∨ S →֒ CP∞ ∨ CP∞ induces a homomorphism f : πm(S 2 ∨ S) −→ πm(CP ∞ ∨ CP∞). We also compute f by evaluating f on each factor in the Hilton splitting of πm(S 2 ∨ S).
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متن کاملar 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
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 corr...
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