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In geometric topology, a branch of mathematics, the lantern relation is a relation that appears between certain Dehn twists in the mapping class group of a surface. The most general version of the relation involves seven Dehn twists. ==General form== The general form of the lantern relation involves seven Dehn twists in the mapping class group of a disk with three holes, as shown in the figure on the right. According to the relation, :, where , , and are the right-handed Dehn twists around the blue curves , , and , and , , , are the right-handed Dehn twists around the four red curves. Note that the Dehn twists , , , on the right-hand side all commute (since the curves are disjoint, so the order in which they appear does not matter. However, the cyclic order of the three Dehn twists on the left does matter: :. Also, note that the equalities written above are actually equality up to homotopy or isotopy, as is usual in the mapping class group. 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「Lantern relation」の詳細全文を読む スポンサード リンク
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