Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry

Chao Wang; Shi Cheng Wang; Yi Mu Zhang; Bruno Zimmermann

doi:10.1007/s11425-017-9078-0

Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry

Chao Wang, Shi Cheng Wang, Yi Mu Zhang, Bruno Zimmermann

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

3 Scopus citations

Abstract

The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space ℝ³ are easier to feel by human’s intuition. We give the maximum order of finite group actions on (ℝ³, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in ℝ³. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.

Original language	English
Pages (from-to)	1599-1614
Number of pages	16
Journal	Science China Mathematics
Volume	60
Issue number	9
DOIs	https://doi.org/10.1007/s11425-017-9078-0
State	Published - 4 May 2017
Externally published	Yes

Keywords

extendable action
finite group action
maximum order
symmetry of surface

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10.1007/s11425-017-9078-0

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title = "Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry",

abstract = "The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space ℝ3 are easier to feel by human{\textquoteright}s intuition. We give the maximum order of finite group actions on (ℝ3, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in ℝ3. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.",

keywords = "extendable action, finite group action, maximum order, symmetry of surface",

author = "Chao Wang and Wang, \{Shi Cheng\} and Zhang, \{Yi Mu\} and Bruno Zimmermann",

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AU - Wang, Chao

AU - Wang, Shi Cheng

AU - Zhang, Yi Mu

AU - Zimmermann, Bruno

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Y1 - 2017/5/4

N2 - The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space ℝ3 are easier to feel by human’s intuition. We give the maximum order of finite group actions on (ℝ3, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in ℝ3. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.

AB - The symmetries of surfaces which can be embedded into the symmetries of the 3-dimensional Euclidean space ℝ3 are easier to feel by human’s intuition. We give the maximum order of finite group actions on (ℝ3, Σ) among all possible embedded closed/bordered surfaces with given geometric/algebraic genus greater than 1 in ℝ3. We also identify the topological types of the bordered surfaces realizing the maximum order, and find simple representative embeddings for such surfaces.

KW - extendable action

KW - finite group action

KW - maximum order

KW - symmetry of surface

UR - https://www.scopus.com/pages/publications/85018794941

U2 - 10.1007/s11425-017-9078-0

DO - 10.1007/s11425-017-9078-0

M3 - 文章

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VL - 60

SP - 1599

EP - 1614

JO - Science China Mathematics

JF - Science China Mathematics

IS - 9

ER -

Embedding compact surfaces into the 3-dimensional Euclidean space with maximum symmetry

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Keywords

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