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

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

16 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1001-1045
Number of pages	45
Journal	Groups, Geometry, and Dynamics
Volume	9
Issue number	4
DOIs	https://doi.org/10.4171/GGD/334
State	Published - 2015
Externally published	Yes

Keywords

3-orbifolds
Extendable action
Maximal order
Surface symmetry

Access to Document

10.4171/GGD/334

Cite this

@article{db8ce0b99fe34deda8e22e0846081bb2,

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",

volume = "9",

pages = "1001--1045",

journal = "Groups, Geometry, and Dynamics",

issn = "1661-7207",

publisher = "European Mathematical Society Publishing House",

number = "4",

}

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

U2 - 10.4171/GGD/334

DO - 10.4171/GGD/334

M3 - 文章

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this