Embedding surfaces into S3 with maximum symmetry

Chao Wang; Shicheng Wang; Yimu Zhang; Bruno Zimmermann

doi:10.4171/GGD/334

Embedding surfaces into S³ with maximum symmetry

Chao Wang
, Shicheng Wang
, Yimu Zhang
, Bruno Zimmermann

Peking University
University of Trieste

科研成果: 期刊稿件 › 文章 › 同行评审

16 引用（Scopus）

摘要

We restrict our discussion to the orientable category. For g > 1, let OE_g be the maximum order of a finite group G acting on the closed surface Σ_g of genus g which extends over.S³; Σ_g), for all possible embeddings Σ_g S³. We will determine OE_g for each g, indeed the action realizing OE_g. In particular, with 23 exceptions, OEg is 4(g + 1) if g ≠ k² or 4 (√g + 1)² if g = k², and moreover OE_g can be realized by unknotted embeddings for all g except for g = 21 and 481.

源语言	英语
页（从-至）	1001-1045
页数	45
期刊	Groups, Geometry, and Dynamics
卷	9
期	4
DOI	https://doi.org/10.4171/GGD/334
出版状态	已出版 - 2015
已对外发布	是

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title = "Embedding surfaces into S3 with maximum symmetry",

abstract = "We restrict our discussion to the orientable category. For g > 1, let OEg be the maximum order of a finite group G acting on the closed surface Σg of genus g which extends over.S3; Σg), for all possible embeddings Σg S3. We will determine OEg for each g, indeed the action realizing OEg. In particular, with 23 exceptions, OEg is 4(g + 1) if g ≠ k2 or 4 (√g + 1)2 if g = k2, and moreover OEg can be realized by unknotted embeddings for all g except for g = 21 and 481.",

keywords = "3-orbifolds, Extendable action, Maximal order, Surface symmetry",

author = "Chao Wang and Shicheng Wang and Yimu Zhang and Bruno Zimmermann",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2015",

doi = "10.4171/GGD/334",

language = "英语",

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pages = "1001--1045",

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TY - JOUR

T1 - Embedding surfaces into S3 with maximum symmetry

AU - Wang, Chao

AU - Wang, Shicheng

AU - Zhang, Yimu

AU - Zimmermann, Bruno

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2015

Y1 - 2015

N2 - We restrict our discussion to the orientable category. For g > 1, let OEg be the maximum order of a finite group G acting on the closed surface Σg of genus g which extends over.S3; Σg), for all possible embeddings Σg S3. We will determine OEg for each g, indeed the action realizing OEg. In particular, with 23 exceptions, OEg is 4(g + 1) if g ≠ k2 or 4 (√g + 1)2 if g = k2, and moreover OEg can be realized by unknotted embeddings for all g except for g = 21 and 481.

AB - We restrict our discussion to the orientable category. For g > 1, let OEg be the maximum order of a finite group G acting on the closed surface Σg of genus g which extends over.S3; Σg), for all possible embeddings Σg S3. We will determine OEg for each g, indeed the action realizing OEg. In particular, with 23 exceptions, OEg is 4(g + 1) if g ≠ k2 or 4 (√g + 1)2 if g = k2, and moreover OEg can be realized by unknotted embeddings for all g except for g = 21 and 481.

KW - 3-orbifolds

KW - Extendable action

KW - Maximal order

KW - Surface symmetry

UR - https://www.scopus.com/pages/publications/84947926315

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DO - 10.4171/GGD/334

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AN - SCOPUS:84947926315

SN - 1661-7207

VL - 9

SP - 1001

EP - 1045

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 4

ER -

Embedding surfaces into S3 with maximum symmetry

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Embedding surfaces into S³ with maximum symmetry