Totally knotted Seifert surfaces with accidental peripherals |
| |
Authors: | Makoto Ozawa Yukihiro Tsutsumi |
| |
Institution: | Department of Mathematics, School of Education, Waseda University, Nishiwaseda 1-6-1, Shinjuku-ku, Tokyo 169-8050, Japan ; Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan |
| |
Abstract: | We show that if there exists an essential accidental surface in the knot exterior, then a closed accidental surface also exists. As its corollary, we know boundary slopes of accidental essential surfaces are integral or meridional. It is shown that an accidental incompressible Seifert surface in knot exteriors in is totally knotted. Examples of satellite knots with arbitrarily high genus Seifert surfaces with accidental peripherals are given, and a Haken 3-manifold which contains a hyperbolic knot with an accidental incompressible Seifert surface of genus one is also given. |
| |
Keywords: | Accidental peripheral quasi-Fuchsian Seifert surface totally knotted |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 |
|