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^*

^*Corresponding author for this work

Northeast Normal University
Dalian Minzu University

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Article number	1750024
Journal	Journal of Knot Theory and its Ramifications
Volume	26
Issue number	5
DOIs	https://doi.org/10.1142/S0218216517500249
State	Published - 1 Apr 2017
Externally published	Yes

Keywords

Curve complex
metrics
torus flow

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10.1142/S0218216517500249

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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.

KW - Curve complex

KW - metrics

KW - torus flow

UR - https://www.scopus.com/pages/publications/85018666125

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DO - 10.1142/S0218216517500249

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 5

M1 - 1750024

ER -

The subset of R³ not realizing metrics on the curve complex

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Keywords

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