On the generalized Massey–Rolfsen invariant for link maps

Skopenkov, A.

Skopenkov, A.

Fundamenta Mathematicae, Tome 163 (2000), p. 1-15 / Harvested from The Polish Digital Mathematics Library

Résumé

For $K = K_{1} ⊔ . . . ⊔ K_{s}$ and a link map $f : K \to ℝ^{m}$ let $K^{\sim} = ⊔_{i < j} K_{i} \times K_{j}$ , define a map $f^{\sim} : K^{\sim} \to S^{m - 1}$ by $f^{\sim} (x, y) = (f x - f y) / | f x - f y |$ and a (generalized) Massey-Rolfsen invariant $α (f) \in π^{m - 1} (K)$ to be the homotopy class of $f^{\sim}$ . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps $f : K \to ℝ^{m}$ up to link concordance to $π^{m - 1} (K^{\sim})$ . If $K_{1}, . . ., K_{s}$ are closed highly homologically connected manifolds of dimension $p_{1}, . . ., p_{s}$ (in particular, homology spheres), then $π^{m - 1} (K^{\sim}) ≅ \oplus_{i < j} π_{p_{i} + p_{j} - m + 1}^{S}$ .

Publié le : 2000-01-01

Zbl 0966.57028

EUDML-ID : urn:eudml:doc:212458

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     author = {A. Skopenkov},
     title = {On the generalized Massey--Rolfsen invariant for link maps},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {1-15},
     zbl = {0966.57028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv165i1p1bwm}
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Skopenkov, A. On the generalized Massey–Rolfsen invariant for link maps. Fundamenta Mathematicae, Tome 163 (2000) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv165i1p1bwm/

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