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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Seifert conjecture ： ウィキペディア英語版 Seifert conjecture In mathematics, the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit. It is named after Herbert Seifert. In a 1950 paper, Seifert asked if such a vector field exists, but did not phrase non-existence as a conjecture. He also established the conjecture for perturbations of the Hopf fibration. The conjecture was disproven in 1974 by Paul Schweitzer, who exhibited a $C^1$ counterexample. Schweitzer's construction was then modified by Jenny Harrison in 1988 to make a $C^$ counterexample for some $\backslash delta\; >\; 0$. The existence of smoother counterexamples remained an open question until 1993 when Krystyna Kuperberg constructed a very different $C^\backslash infty$ counterexample. Later this construction was shown to have real analytic and piecewise linear versions. ==References== *V. Ginzburg and B. Gürel, ''(A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $R^4$ )'', Ann. of Math. (2) 158 (2003), no. 3, 953--976 *J. Harrison, ''$C^2$ counterexamples to the Seifert conjecture'', Topology 27 (1988), no. 3, 249--278. *G. Kuperberg ''A volume-preserving counterexample to the Seifert conjecture'', Comment. Math. Helv. 71 (1996), no. 1, 70--97. *K. Kuperberg ''A smooth counterexample to the Seifert conjecture'', Ann. of Math. (2) 140 (1994), no. 3, 723--732. *G. Kuperberg and K. Kuperberg, ''(Generalized counterexamples to the Seifert conjecture )'', Ann. of Math. (2) 143 (1996), no. 3, 547--576. *H. Seifert, ''Closed integral curves in 3-space and isotopic two-dimensional deformations'', Proc. Amer. Math. Soc. 1, (1950). 287--302. *P. A. Schweitzer, ''Counterexamples to the Seifert conjecture and opening closed leaves of foliations'', Ann. of Math. (2) 100 (1974), 386--400. 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「Seifert conjecture」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.