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Displaying similar documents to “A product involving the β -family in stable homotopy theory.”

Homotopy and homology groups of the n-dimensional Hawaiian earring

Katsuya Eda, Kazuhiro Kawamura (2000)

Fundamenta Mathematicae

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For the n-dimensional Hawaiian earring ℍ n , n ≥ 2, π n ( ℍ n , o ) ≃ ℤ ω and π i ( ℍ n , o ) is trivial for each 1 ≤ i ≤ n - 1. Let CX be the cone over a space X and CX ∨ CY be the one-point union with two points of the base spaces X and Y being identified to a point. Then H n ( X ∨ Y ) ≃ H n ( X ) ⊕ H n ( Y ) ⊕ H n ( C X ∨ C Y ) for n ≥ 1.

On the generalized Massey–Rolfsen invariant for link maps

A. Skopenkov (2000)

Fundamenta Mathematicae

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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 ) = ( f x - f y ) / | f x - f y | 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 p i + p j - m + 1 S .

The homotopy type of the space of degree 0 immersed plane curves.

Hiroki Kodama, Peter W. Michor (2006)

Revista Matemática Complutense

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The space B = Imm (S, R) / Diff (S) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups π(B ) = Z, π(B ) = Z, and π(B ) = 0 for k ≥ 3.