Coincidences for maps of spaces with finite group actions

Gonçalves, Daciberg Lima; Jaworowski, Jan; Pergher, Pedro L. Q.; Volovikov, A Yu

doi:10.1016/j.topol.2004.05.010

Cited by 12 publications

(7 citation statements)

References 6 publications

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“…If H is a subgroup of G, then H acts on the right on each orbit Gx of G as follows: if y ∈ Gx and y = gx, g ∈ G, then hy = ghx (such action may depend on the choice of the reference point x). Following [4], [6], [9] the concept of G-coincidence is generalized as follows: a point x ∈ X is said to be a (H, G)-coincidence point of f if f sends every orbit of the action of H on the G-orbit of x to a single point (see [5]). We will denote by A(f, H, G) the set of all (H, G)-coincidence points of f .…”

Section: (H G)-coincidencementioning

confidence: 99%

On nonsymmetric theorems for $(H,G)$-coincidences

Mattos¹,

Santos²

2009

TMNA

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Let X be a compact Hausdorff space, ϕ: X → S n a continuous map into the n-sphere S n that induces a nonzero homomorphism ϕ * : H n (S n ; Zp) → H n (X; Zp), Y a k-dimensional CW-complex and f : X → Y a continuous map. Let G a finite group which acts freely on S n. Suppose that H ⊂ G is a normal cyclic subgroup of a prime order. In this paper, we define and we estimate the cohomological dimension of the set Aϕ(f, H, G) of (H, G)-coincidence points of f relative to ϕ.

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Section: (H G)-coincidencementioning

confidence: 99%

On nonsymmetric theorems for $(H,G)$-coincidences

Mattos¹,

Santos²

2009

TMNA

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“…In the second direction are the papers of Izydorek and Jaworowski [10] (for H = G = Z p , X = S n and Y a CW-complex ), Gonçalves and Pergher [7] (for H = G = Z p , X = S n and Y a CW-complex ) and for proper nontrivial subgroup H of G, Gonçalves, Jaworowski and Pergher [8] (for H = Z p subgroup of a finite group G, X an homotopy sphere and Y a CW-complex) and Gonçalves, Jaworowski, Pergher and Volovikov [9](for H = Z p subgroup of a finite group G, X under certain (co)homological assumptions and Y a CW-complex).…”

Section: Introductionmentioning

confidence: 99%

$(H,G)$-coincidence theorems for manifolds and a topological Tverberg type theorem for any natural number $r$

Mattos¹,

Santos²,

Souza³

2017

Bull. Belg. Math. Soc. Simon Stevin

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Let X be a paracompact space, let G be a finite group acting freely on X and let H a cyclic subgroup of G of prime order p. Let f :In this work, we estimate the cohomological dimension of the set A(f, H, G) of (H, G)-coincidence points of f . Also, we estimate the index of a (H, G)coincidence set in the case that H is a p-torus subgroup of a particular group G and as application we prove a topological Tverberg type theorem for any natural number r. Such result is a weak version of the famous topological Tverberg conjecture, which was proved recently, fail for all r that are not prime powers. Moreover, we obtain a generalized Van Kampen-Flores type theorem for any natural number r. main directions considered of this problem are either when the target space Y is a manifold or Y is a CW complex. In the first direction are the papers of Borsuk [4] ( the classical theorem of Borsuk-Ulam, for H = G = Z 2 , X = S n and Y = R n ), Conner and Floyd [5] (for H = G = Z 2 and Y a n-manifold), Munkholm [13] (for H = G = Z p , X = S n and Y = R m ), Nakaoka [14] (for H = G = Z p , X under certain (co)homological conditions and Y a m-manifold) and the following more general version proved by Volovikov [17] using the index of a free Z p -space X (ind X, see Definition 2.2 ):Theorem A.[17, Theorem 1.2] Let X be a paracompact free Z p -space of ind X ≥ n, and f : X → M a continuous mapping of X into an m-dimensional connected manifold M (orientable if p > 2). Assume that:

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“…Na formulação geral acima de G-coincidência quando o domínio X e um espaço satisfazendo determinadas condições e contradomínio Ý e um CW -complexo, o problema foi abordado em vários artigos, a saber, [7,8,9,10], [13,14] e [21].…”

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Teorema de Borsuk-Ulam para formas espaciais esféricas

Santos¹

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Coincidences for maps of spaces with finite group actions

Cited by 12 publications

References 6 publications

On nonsymmetric theorems for $(H,G)$-coincidences

On nonsymmetric theorems for $(H,G)$-coincidences

$(H,G)$-coincidence theorems for manifolds and a topological Tverberg type theorem for any natural number $r$

Teorema de Borsuk-Ulam para formas espaciais esféricas

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