塚本 達也 (Tatsuya TSUKAMOTO) 大阪工業大学 工学部 一般教育科
535-8585 大阪市旭区大宮 5-16-1
Email: email address


研究会「Knots in east Osaka VI」

日時:2013年2月23日(土)
場所:大阪工業大学 大宮キャンパス 6号館 681教室

プログラム( PDFファイル
13:00-13:40 安原 晃(東京学芸大学)絡み目の自己局所変形について
14:00-14:40 金信 泰造(大阪市立大学)Links which are related by a band surgery
15:00-15:40 中西 康剛(神戸大学)A note on Hamilton knot projection
16:00-16:40 河内 明夫(大阪市立大学)An example of a 4-manifold with every closed 3-manifold embedded
17:00-17:40 渋谷 哲夫(大阪工業大学)Genera of links related by a simple ribbon fusion

18:00 より 6号館 15階ルラーシュにて懇親会を予定しております.
この懇親会は今年度で大阪工業大学を退職される渋谷哲夫先生のお祝いを兼ねております.

世話人
塚本 達也(大阪工業大学)
岸本 健吾(大阪工業大学)
中村 拓司(大阪電気通信大学)



アブストラクト

安原 晃 (東京学芸大学) 絡み目の自己局所変形について
自己パス変形や自己デルタ変形は,絡み目のリンク・ホモトピーの一般化として渋谷先生により定義された絡み目の局所変形である. 本講演では,これらの局所変形に関してこれまでに得られた結果を,渋谷先生との共同研究を中心に紹介する.

金信 泰造 (大阪市立大学) Links which are related by a band surgery
We introduce some criteria for two links, which are related by a band surgery or crossing change, using the determinant and the Jones polynomials. We also give an improved table of H(2)-Gordian distances between knots with up to seven crossings. This is a joint work with Hiromasa Moriuchi.

中西 康剛 (神戸大学) A note on Hamilton knot projection
This is a joint work with R. Higa and R. Nakanishi. Diao, Ernst, and Yu have studied which kinds of knot projections are Hamiltonian, and show that every knot type has a Hamilton knot projection with at most 4cr(K) crossings, where cr(K) means the minimum crossing number of K. In this talk, we will show that every knot type has a Hamilton knot projection with at most 2cr(K)-3 crossings.

河内 明夫 (大阪市立大学) An example of a 4-manifold with every closed 3-manifold embedded
An example of a 4-manifold with every closed 3-manifold embedded. An embedding f from a closed orientable 3-manifold M into an open orientable 4-manifold X is called a type I or type II embedding according to whether the complement X-f(M) is connected or not, respectively. In this talk, we discuss an example of an open orientable 4-manifold with every closed orientable 3-manifold embedded by a type I embedding in which a closed orientable 3-manifold cannot be embedded by any type II embedding.

渋谷 哲夫 (大阪工業大学) Genera of links related by a simple ribbon fusion
For an oriented link l in the 3-sphere, there is a Seifert surface of l. The disconnectivity number of l, denoted by ν(l), means the maximum number of connected components of Seifert surfaces of l. For each integer r (1≦r≦ν(l)), there is a Seifert surface F of l with ♯(F)=r. The r-th genus of l, denoted by gr(l), means the minimum number of genera among these Seifert surfaces of l with ♯(F)=r. We study the relations of disconnectivity numbers and genera of links l and L such that L is obtained from l by a simple ribbon fusion and show that ν(L)≦ν(L) and gr(L)gr(l) and that, if ν(L)=ν(L)=s and gr(L)=gr(l), then l is ambient isotopic to L. This is a joint work with K. Kishimoto and T. Tsukamoto.



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