- Tytuł:
- On the generalized Massey–Rolfsen invariant for link maps
- Autorzy:
- Skopenkov, A.
- Powiązania:
- https://bibliotekanauki.pl/articles/1205018.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
deleted product
Massey-Rolfsen invariant
link maps
link homotopy
stable homotopy group
double suspension
codimension two
highly connected manifolds - Opis:
- 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 $π^{m-1}(K^∼)≅⊕_{i < j} π^S_{p_i + p_j - m + 1}$.
- Źródło:
-
Fundamenta Mathematicae; 2000, 165, 1; 1-15
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł