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2000 | 165 | 1 | 1-15
Tytuł artykułu

On the generalized Massey–Rolfsen invariant for link maps

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For $K = K_1⊔...⊔K_s$ and a link map $f:K → ℝ^m$ let $K^∼ = ⊔_{i < j} K_i × K_j$, define a map $f^∼ : K^∼ → S^{m - 1}$ by $f^∼(x, y) = (fx - fy)/|fx - fy|$ and a (generalized) Massey-Rolfsen invariant $α(f) ∈ π^{m - 1}(K)$ to be the homotopy class of $f^∼$. 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 $f:K → ℝ^m$ up to link concordance to $π^{m - 1}(K^∼)$. If $K_1,...,K_s$ are closed highly homologically connected manifolds of dimension $p_1,...,p_s$ (in particular, homology spheres), then $π^{m-1}(K^∼)≅⊕_{i < j} π^S_{p_i + p_j - m + 1}$.
Rocznik
Tom
165
Numer
1
Strony
1-15
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-05-21
poprawiono
1998-10-02
poprawiono
2000-03-14
Twórcy
autor
  • Department of Differential Geometry, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia 119899, skopenko@mccme.ru
Bibliografia
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Bibliografia
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