Extending finite group actions on surfaces over S3

Chao Wang; Shicheng Wang; Yimu Zhang; Bruno Zimmermann

doi:10.1016/j.topol.2013.08.014

Extending finite group actions on surfaces over S³

Chao Wang, Shicheng Wang, Yimu Zhang, Bruno Zimmermann

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

15 Scopus citations

Abstract

Let OE_g (resp. CE_g and AE_g) and resp. OEgo be the maximum order of finite (resp. cyclic and abelian) groups G acting on the closed orientable surfaces σ_g which extend over (S³, σ_g) among all embeddings σ_g→S³ and resp. unknotted embeddings σ_g→S³.It is known that OEgo≤12(g-1), and we show that 12(g-1) is reached for an unknotted embedding σ_g→S³ if and only if g=2, 3, 4, 5, 6, 9, 11, 17, 25, 97, 121, 241, 601. Moreover AE_g is 2g+2; and CE_g is 2g+2 for even g, and 2g-2 for odd g.Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere.

Original language	English
Pages (from-to)	2088-2103
Number of pages	16
Journal	Topology and its Applications
Volume	160
Issue number	16
DOIs	https://doi.org/10.1016/j.topol.2013.08.014
State	Published - 1 Oct 2013
Externally published	Yes

Keywords

Extendable action
Finite group action
Maximum order
Symmetry of 3-sphere
Symmetry of surface

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10.1016/j.topol.2013.08.014

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title = "Extending finite group actions on surfaces over S3",

abstract = "Let OEg (resp. CEg and AEg) and resp. OEgo be the maximum order of finite (resp. cyclic and abelian) groups G acting on the closed orientable surfaces σg which extend over (S3, σg) among all embeddings σg→S3 and resp. unknotted embeddings σg→S3.It is known that OEgo≤12(g-1), and we show that 12(g-1) is reached for an unknotted embedding σg→S3 if and only if g=2, 3, 4, 5, 6, 9, 11, 17, 25, 97, 121, 241, 601. Moreover AEg is 2g+2; and CEg is 2g+2 for even g, and 2g-2 for odd g.Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere.",

keywords = "Extendable action, Finite group action, Maximum order, Symmetry of 3-sphere, Symmetry of surface",

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

year = "2013",

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day = "1",

doi = "10.1016/j.topol.2013.08.014",

language = "英语",

volume = "160",

pages = "2088--2103",

journal = "Topology and its Applications",

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TY - JOUR

T1 - Extending finite group actions on surfaces over S3

AU - Wang, Chao

AU - Wang, Shicheng

AU - Zhang, Yimu

AU - Zimmermann, Bruno

PY - 2013/10/1

Y1 - 2013/10/1

N2 - Let OEg (resp. CEg and AEg) and resp. OEgo be the maximum order of finite (resp. cyclic and abelian) groups G acting on the closed orientable surfaces σg which extend over (S3, σg) among all embeddings σg→S3 and resp. unknotted embeddings σg→S3.It is known that OEgo≤12(g-1), and we show that 12(g-1) is reached for an unknotted embedding σg→S3 if and only if g=2, 3, 4, 5, 6, 9, 11, 17, 25, 97, 121, 241, 601. Moreover AEg is 2g+2; and CEg is 2g+2 for even g, and 2g-2 for odd g.Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere.

AB - Let OEg (resp. CEg and AEg) and resp. OEgo be the maximum order of finite (resp. cyclic and abelian) groups G acting on the closed orientable surfaces σg which extend over (S3, σg) among all embeddings σg→S3 and resp. unknotted embeddings σg→S3.It is known that OEgo≤12(g-1), and we show that 12(g-1) is reached for an unknotted embedding σg→S3 if and only if g=2, 3, 4, 5, 6, 9, 11, 17, 25, 97, 121, 241, 601. Moreover AEg is 2g+2; and CEg is 2g+2 for even g, and 2g-2 for odd g.Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere.

KW - Extendable action

KW - Finite group action

KW - Maximum order

KW - Symmetry of 3-sphere

KW - Symmetry of surface

UR - https://www.scopus.com/pages/publications/84884587084

U2 - 10.1016/j.topol.2013.08.014

DO - 10.1016/j.topol.2013.08.014

M3 - 文章

AN - SCOPUS:84884587084

SN - 0166-8641

VL - 160

SP - 2088

EP - 2103

JO - Topology and its Applications

JF - Topology and its Applications

IS - 16

ER -

Extending finite group actions on surfaces over S³

Abstract

Keywords

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