A note on the converse of the Lefschetz theorem for G-maps

M. Izydorek; A. Vidal

Displaying similar documents to “A note on the converse of the Lefschetz theorem for G-maps”

The topology of the Banach–Mazur compactum

Sergey Antonyan (2000)

Fundamenta Mathematicae

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Let J(n) be the hyperspace of all centrally symmetric compact convex bodies $A \subseteq ℝ^{n}$ , n ≥ 2, for which the ordinary Euclidean unit ball is the ellipsoid of maximal volume contained in A (the John ellipsoid). Let $J_{0} (n)$ be the complement of the unique O(n)-fixed point in J(n). We prove that: (1) the Banach-Mazur compactum BM(n) is homeomorphic to the orbit space J(n)/O(n) of the natural action of the orthogonal group O(n) on J(n); (2) J(n) is an O(n)-AR; (3) $J_{0} (2) / S O (2)$ is an Eilenberg-MacLane space $𝐊 (ℚ, 2)$ ; (4)...

The Nielsen coincidence theory on topological manifolds

Jerzy Jezierski (1993)

Fundamenta Mathematicae

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We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.

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.

On the equivalence of Quillen's and Swan's $K$ -theories.

Ebeling, Paul, Keune, Frans (2002)

Georgian Mathematical Journal

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Decomposing four-manifolds up to homotopy type.

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

Beiträge zur Algebra und Geometrie

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Nielsen theory of transversal fixed point sets (with an appendix: $C^{\infty}$ and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...

Diagonal fibrations are pointwise fibrations.

Cegarra, A.M., Remedios, J. (2007)

Journal of Homotopy and Related Structures

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