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Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds. ==Analogies== The following are some of the analogies used by mathematicians between number fields and 3-manifolds:〔Sikora, Adam S. "Analogies between group actions on 3-manifolds and number fields." Commentarii Mathematici Helvetici 78.4 (2003): 832-844.〕 #A number field corresponds to a closed, orientable 3-manifold #Ideals in the ring of integers correspond to links, and prime ideals correspond to knots. #The field Q of rational numbers corresponds to the 3-sphere. Expanding on the last two examples, there is an analogy between knots and prime numbers in which one considers "links" between primes. The triple of primes are "linked" modulo 2 (the Rédei symbol is −1) but are "pairwise unlinked" modulo 2 (the Legendre symbols are all 1). Therefore these primes have been called a "proper Borromean triple modulo 2" or "mod 2 Borromean primes". 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「arithmetic topology」の詳細全文を読む スポンサード リンク
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