Geometric structures of 3-manifolds and various related structures
Geometric structures of 3-manifolds and various related structures
批准号:
17540077
负责人:
KOBAYASHI Tsuyoshi
金额:
$1.41万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2005
资助国家:
日本
项目状态:
已结题
起止时间:
2005 至 2006
中文摘要
在这个研究项目中,我们决定了一个numerical invariant,called growth rate of tunnel numbers, of knots in 3-manifolds. For m-small knots,we obtained the following.Suppose K is a M -small knot in. a3 -manifold M. Let g = g(X)-g(M)and b_i (i =1,…,g) be the bridge index of K with respect to genus g(X) - i Heegaard surface of M. Then the growthrate of K is given by min_i=_<1,…, n>{1-i/(b_i)}.2. Heegaard splittings of exteriors of knots. Let k_1,k_2 be knots in 3-manifolds, and t_1, t_2 tunnel systems of k_1,k_2 respectively. We gave a necessary and sufficient condition for the tunnel system t_1小区t_2 ofk_2 giving a stabilized Heegaard splitting. For each natural number n,there存在s a knot K such that the equality g(nK) = gt(K) holds,where nK denotes the connected sum of n copies of K. This implies the existence of counterexample toMorimoto's Conjecture concerning super additive phenomina of tunnel number of knots.3. We showedthat for any link L in the 3-sphere,there is a Seifert surface S for L such that S is obtained from a disk by successively plumbing flatannuli,where all of the attaching regions are the disk.4. We made research on Gersten'sproblem:each automatic group is either (1) a finite group,(3) a word hyperbolic group. we showed that for the word hyperbolic group. we showed that for then-starred automatic groups this assertion holds.5. Growth function of 2-bridge link groupsWe madecomputar experiments on the growth functions of 2-bridge link groupsand posed conjectures on the structure of the growth functions
英文摘要
In this research project, we obtained the following results.1. We defined a numerical invariant, called growth rate of tunnel numbers, of knots in 3-manifolds. For m-small knots, we obtained the following.Suppose K is a m-small knot in. a 3-manifold M. Let g = g(X)-g(M), and b_i (i =1,..., g) be the bridge index of K with respect to genus g(X) - i Heegaard surface of M. Then the growth rate of K is given by min_i=_<1,..., n>{1-i/(b_i)}.2. Heegaard splittings of exteriors of knots.・ Let K_1, K_2 be knots in 3-manifolds, and T_1,T_2 tunnel systems of K_1, K_2 respectively. We gave a necessary and sufficient condition for the tunnel system t_1 ∪ T_2 of K_1#K_2 giving a stabilized Heegaard splitting.・ For each natural number n, there exists a knot K such that the equality g(nK) = gt(K) holds, where nK denotes the connected sum of n copies of K. This implies the existence of counterexample to Morimoto's Conjecture concerning super additive phenomina of tunnel number of knots.3. We showed that for any link L in the 3-sphere, there is a Seifert surface S for L such that S is obtained from a disk by successively plumbing flat annuli, where all of the attaching regions are contained in the disk.4. We made research on Gersten's Problem : each automatic group is either (1) a finite group, (2) contains a free abelian group of rank 2. or (3) a word hyperbolic group.We showed that for the n-starred automatic groups this assertion holds.5. Growth function of 2-bridge link groupsWe made computar experiments on the growth functions of 2-bridge link groups, and posed conjectures on the structure of the growth functions.
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DOI:
--
发表时间:
2005
期刊:
Japan.J.Math 31
影响因子:
--
作者:
[M.Brittenham, C.Hayashi, M.Hirasawa, T.Kobayashi, K.Shimokawa]
通讯作者:
K.Shimokawa
DOI:
--
发表时间:
期刊:
Journal fur die Reine and Ang. Math. (to appear)
影响因子:
--
作者:
[Kobayashi, Teiichi, Minyou Katagiri, T.Shibata, Tsuyoshi Kobayashi, T.Kobayashi, Tsuyoshi Kobayashi, S.Matsumoto, T.Inaba, Kazuhiro Ichihara, Tsuyoshi Kobayashi, Kazuhiro Ichihara, Tsuyoshi Kobayashi]
通讯作者:
Tsuyoshi Kobayashi
A search method for a thin position of a link
一种链接细位置的搜索方法
DOI:
--
发表时间:
2005
期刊:
Algebr. Geom. Topol. 5
影响因子:
--
作者:
[T.Kobayashi, Y.Riek, Yasushi Yamashita, Yamashita Yasushi, M.Brittenham, Tsuyoshi Kobayashi]
通讯作者:
Tsuyoshi Kobayashi
Drawing Bers embeddings of the Teichmu}ller space of once-punctured tori
绘制一次刺穿环面 Teichmuller 空间的 Bers 嵌入
DOI:
--
发表时间:
期刊:
Experimental Mathematics (to appear)
影响因子:
--
作者:
[Y.Komori, T.Sugawa, M.Wada, Y.Yamashita]
通讯作者:
Y.Yamashita
DOI:
--
发表时间:
期刊:
Lond. Math. Soc. Lec. Notes (to appear)
影响因子:
--
作者:
[Y.Hemmi, J.Lin, Yasushi Yamashita]
通讯作者:
Yasushi Yamashita
共 6 条
Development of the novel molecular targeted therapy against hepatocellular carcinoma invasion and metastasis
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批准号:21791288
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项目类别:Grant-in-Aid for Young Scientists (B)
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资助金额:$2.58万
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财政年份:2009
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负责人:KOBAYASHI Tsuyoshi
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依托单位:
On developments and applications of Heegaard theory
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批准号:21540082
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.16万
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财政年份:2009
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负责人:KOBAYASHI Tsuyoshi
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依托单位:
Research on 3-manifolds based on geometric techniques and its expanse
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批准号:19540083
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$1.25万
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财政年份:2007
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负责人:KOBAYASHI Tsuyoshi
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依托单位:
Research on various geometric structures on 3-manifolds
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批准号:15540073
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$1.34万
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财政年份:2003
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负责人:KOBAYASHI Tsuyoshi
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依托单位:
Representations of 3-manifolds and geometric informations derived from them
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批准号:12640071
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$1.79万
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财政年份:2000
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负责人:KOBAYASHI Tsuyoshi
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依托单位:
Combinatorial structures of low dimensional manifolds
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批准号:10640076
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项目类别:Grant-in-Aid for Scientific Research (C)
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资助金额:$2.43万
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财政年份:1998
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负责人:KOBAYASHI Tsuyoshi
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依托单位:
海外基金