2 8 M ay 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).
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 ...
متن کاملar 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 کاملun 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), the re...
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...
متن کامل0 M ar 1 99 9 CANONICAL FRAMINGS FOR 3 - MANIFOLDS
A framing of an oriented trivial bundle is a homotopy class of sections of the associated oriented frame bundle. This paper is a study of the framings of the tangent bundle τM of a smooth closed oriented 3-manifold M , often referred to simply as framings of M .1 We shall also discuss stable framings and 2-framings of M , that is framings of ε1 ⊕ τM (where ε1 is an oriented line bundle) and 2τM...
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تاریخ انتشار 2002