Minimal finite models.

Barmak, Jonathan Ariel; Minian, Elias Gabriel

Displaying similar documents to “Minimal finite models.”

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 $H_{n} (X \lor Y) ≃ H_{n} (X) \oplus H_{n} (Y) \oplus H_{n} (C X \lor C Y)$ for n ≥ 1.

Generalized homotopy in C-categories.

F. J. Díaz, J. Remedios, S. Rodríguez-Machín (2001)

Extracta Mathematicae

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Homotopy theory induced by cones.

F. J. Díaz, S. Rodríguez-Machín (2001)

Extracta Mathematicae

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Cochain operations defining Steenrod- $⌣_{i}$ -products in the bar construction.

Kadeishvili, T. (2003)

Georgian Mathematical Journal

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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.

Decomposing four-manifolds up to homotopy type.

Cavicchioli, Alberto, Ruini, Beatrice, Spaggiari, Fulvia (2003)

Beiträge zur Algebra und Geometrie

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On constructing resolutions over the polynomial algebras.

Johansson, Leif, Lambe, Larry, Sköldberg, Emil (2002)

Homology, Homotopy and Applications

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Note on the rational cohomology of the function space of based maps.

Kotani, Yasusuke (2004)

Homology, Homotopy and Applications

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Reparametrizations of continuous paths.

Fahrenberg, U., Raussen, M. (2007)

Journal of Homotopy and Related Structures

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Cores of spaces, spectra, and $E_{\infty}$ ring spectra.

Hu, P., Kriz, I., May, J.P. (2001)

Homology, Homotopy and Applications

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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 $f : K \to ℝ^{m}$ 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 $π^{m - 1} (K^{\sim}) ≅ \oplus_{i < j} π_{p_{i} + p_{j} - m + 1}^{S}$ .