The subset of R3 not realizing metrics on the curve complex

Faze Zhang; Yanqing Zou

doi:10.1142/S0218216517500249

The subset of R³ not realizing metrics on the curve complex

Faze Zhang
, Yanqing Zou^*

^*此作品的通讯作者

Northeast Normal University
Dalian Minzu University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In [F. Zhang, R. Qiu and Y. Zou, The subset of R³ realizing metrics on the curve complex, Topology Appl. 193 (2015) 259-269], they defined a subset of R³ and a metric d_N through each point of for the curve complex (S). For further understanding the curve complex, we concern the whole set R³. With adaption to the flow theory on torus, we prove that for any point of R³ -, the d_N is not a metric on (S) or 0(S). This means that the is the maximal subset of R³ realizing metrics on the curve complex.

源语言	英语
文章编号	1750024
期刊	Journal of Knot Theory and its Ramifications
卷	26
期	5
DOI	https://doi.org/10.1142/S0218216517500249
出版状态	已出版 - 1 4月 2017
已对外发布	是

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abstract = "In [F. Zhang, R. Qiu and Y. Zou, The subset of R3 realizing metrics on the curve complex, Topology Appl. 193 (2015) 259-269], they defined a subset of R3 and a metric dN through each point of for the curve complex (S). For further understanding the curve complex, we concern the whole set R3. With adaption to the flow theory on torus, we prove that for any point of R3 -, the dN is not a metric on (S) or 0(S). This means that the is the maximal subset of R3 realizing metrics on the curve complex.",

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AB - In [F. Zhang, R. Qiu and Y. Zou, The subset of R3 realizing metrics on the curve complex, Topology Appl. 193 (2015) 259-269], they defined a subset of R3 and a metric dN through each point of for the curve complex (S). For further understanding the curve complex, we concern the whole set R3. With adaption to the flow theory on torus, we prove that for any point of R3 -, the dN is not a metric on (S) or 0(S). This means that the is the maximal subset of R3 realizing metrics on the curve complex.

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KW - metrics

KW - torus flow

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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M1 - 1750024

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The subset of R3 not realizing metrics on the curve complex

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The subset of R³ not realizing metrics on the curve complex