满足 g(E(K)) = 2 且 g(E(K#K#K)) = 6 的纽结与森本猜想
几何拓扑
2007-05-23 v3
摘要
我们证明在 S^3 中存在纽结 K,满足 g(E(K))=2 且 g(E(K#K#K))=6。结合 [1] 的定理 1.5,这证明了森本猜想(Conjecture 1.5 of [2])的反例的存在性。这是 arxiv.org/abs/math.GT/0701765 的一个特例。[1] Tsuyoshi Kobayashi and Yo'av Rieck. On the growth rate of the tunnel number of knots. J. Reine Angew. Math., 592:63--78, 2006. [2] Kanji Morimoto. On the super additivity of tunnel number of knots.Math. Ann., 317(3):489--508, 2000.
关键词
引用
@article{arxiv.math/0701766,
title = {Knots with g(E(K)) = 2 and g(E(K#K#K)) = 6 and Morimoto's Conjecture},
author = {Tsuyoshi Kobayashi and Yo'av Rieck},
journal= {arXiv preprint arXiv:math/0701766},
year = {2007}
}
备注
6 pages. Final version