Research on Structures of Knots and Manifolds as Models
Grant-in-Aid for Scientific Research (B)
|Research Institution||Kobe University|
NAKANISHI Yasutaka Kobe University Faculty of Sciences Professor, 理学部, 教授 (70183514)
SAITO Masa-hiko Kobe University Faculty of Sciences Professor, 理学部, 教授 (80183044)
TAKAYAMA Nobuki Kobe University Faculty of Sciences Professor, 理学部, 教授 (30188099)
NOUMI Masatoshi Kobe University Faculty of Sciences Professor, 理学部, 教授 (80164672)
NAGURA Toshinobu Kobe University Faculty of Sciences Assistant, 理学部, 助手 (50116232)
IKEDA Hiroshi Kobe University Faculty of Sciences Professor, 理学部, 教授 (10031353)
|Project Fiscal Year
1996 – 1996
Completed(Fiscal Year 1996)
|Budget Amount *help
¥4,000,000 (Direct Cost : ¥4,000,000)
Fiscal Year 1996 : ¥4,000,000 (Direct Cost : ¥4,000,000)
|Keywords||Model / Knot / Manifold / Alexander invariant / Geometric structure / Unknotting operation / 模型 / 結び目 / 多様体 / Alexander不変量 / 幾何構造 / 結び目解消操作|
According to the purpose and operating plan of the above project, the head investigator has obtained the following results.
1.For two-bridge knots, necessary conditions on coefficients of Alexander polynomials are given.
2.Shibuya's result that any union of two nontrivial knots without local knots is prime is proved in a general setting by tangle arguments. And the concrete example of exception are given.
3.For every minimum-crossing knot-diagram among all unknotting-number-one two-bridge knots, the existence of crossings whose exchange yields the trivial knot is proved. This result is a part of answer of a conjecture on unknotting number.
These results 1,2, and are published.
4.The Delta-unknotting numbers for torus knots, positive closed 3-braids, and positive protzel knots are determined.
5.The borromean rings and the 3-component trivial link cannot be deformable to each other by a finite sequence of link-homotopies and cancellations of consecutive 4-crossings.
These results 4 and 5 are accepted to be published.
He gave lectures based on the above results at international conferences : Conference/Workshop for The Fifth MSJ International Research Instutute Knot Theory (Waseda University, 1996.7.22-31), The fifth Japan-Korea Seminar on Knots and Links (Korean Advansed Institute for Science and Technology, 1997.2.17-20).
Furthemore all investigators have obtained their results according to their roles.
Research Output (18results)