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In mathematics, topological Galois theory is a mathematical theory which originated from a topological proof of Abel's impossibility theorem found by V. I. Arnold and concerns the applications of some topological concepts to some problems in the field of Galois theory. It connects many ideas from algebra to ideas in topology. As described in Khovanskii's book: "According to this theory, the way the Riemann surface of an analytic function covers the plane of complex numbers can obstruct the representability of this function by explicit formulas. The strongest known results on the unexpressibility of functions by explicit formulas have been obtained in this way."

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  • Teoria de Galois topológica (pt)
  • Topological Galois theory (en)
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  • In mathematics, topological Galois theory is a mathematical theory which originated from a topological proof of Abel's impossibility theorem found by V. I. Arnold and concerns the applications of some topological concepts to some problems in the field of Galois theory. It connects many ideas from algebra to ideas in topology. As described in Khovanskii's book: "According to this theory, the way the Riemann surface of an analytic function covers the plane of complex numbers can obstruct the representability of this function by explicit formulas. The strongest known results on the unexpressibility of functions by explicit formulas have been obtained in this way." (en)
  • Em matemática, a teoria de Galois topológica é uma teoria matemática que se originou a partir de uma demonstração topológica do teorema da impossibilidade de Abel descoberta por V. I. Arnold, e diz respeito a aplicações de alguns conceitos topológicos para alguns problemas no campo da teoria de Galois. Ela conecta muitas idéias da álgebra a ideias da topologia. Como descrito no livro de Khovanskii: "De acordo com esta teoria, a forma como a superfície de Riemann de uma função analítica cobre o plano dos números complexos pode obstruir a representatividade desta função por fórmulas explícitas. Os mais fortes resultados conhecidos sobre a inexpressibilidade de funções por fórmulas explícitas foram obtidos desta maneira." (pt)
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  • In mathematics, topological Galois theory is a mathematical theory which originated from a topological proof of Abel's impossibility theorem found by V. I. Arnold and concerns the applications of some topological concepts to some problems in the field of Galois theory. It connects many ideas from algebra to ideas in topology. As described in Khovanskii's book: "According to this theory, the way the Riemann surface of an analytic function covers the plane of complex numbers can obstruct the representability of this function by explicit formulas. The strongest known results on the unexpressibility of functions by explicit formulas have been obtained in this way." (en)
  • Em matemática, a teoria de Galois topológica é uma teoria matemática que se originou a partir de uma demonstração topológica do teorema da impossibilidade de Abel descoberta por V. I. Arnold, e diz respeito a aplicações de alguns conceitos topológicos para alguns problemas no campo da teoria de Galois. Ela conecta muitas idéias da álgebra a ideias da topologia. Como descrito no livro de Khovanskii: "De acordo com esta teoria, a forma como a superfície de Riemann de uma função analítica cobre o plano dos números complexos pode obstruir a representatividade desta função por fórmulas explícitas. Os mais fortes resultados conhecidos sobre a inexpressibilidade de funções por fórmulas explícitas foram obtidos desta maneira." (pt)
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