Extending periodic automorphisms of surfaces to 3-manifolds

Yi Ni; Chao Wang; Shicheng Wang

doi:10.4310/CAG.241015032653

Extending periodic automorphisms of surfaces to 3-manifolds

Yi Ni, Chao Wang, Shicheng Wang

School of Mathematical Sciences

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

2 Scopus citations

Abstract

In the orientable category, we show that, if a finite group G acts on a closed surface Σ so that each element of it is extendable over the 3-sphere S³as a diffeomorphism with respect to a fixed embedding Σ → S³, then G is extendable over S³as a group action with respect to some other embedding Σ → S³. Degree one maps are involved in the proof.

Original language	English
Pages (from-to)	889-921
Number of pages	33
Journal	Communications in Analysis and Geometry
Volume	32
Issue number	3
DOIs	https://doi.org/10.4310/CAG.241015032653
State	Published - 2024

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10.4310/CAG.241015032653

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title = "Extending periodic automorphisms of surfaces to 3-manifolds",

abstract = "In the orientable category, we show that, if a finite group G acts on a closed surface Σ so that each element of it is extendable over the 3-sphere S3as a diffeomorphism with respect to a fixed embedding Σ → S3, then G is extendable over S3as a group action with respect to some other embedding Σ → S3. Degree one maps are involved in the proof.",

author = "Yi Ni and Chao Wang and Shicheng Wang",

year = "2024",

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T1 - Extending periodic automorphisms of surfaces to 3-manifolds

AU - Ni, Yi

AU - Wang, Chao

AU - Wang, Shicheng

PY - 2024

Y1 - 2024

N2 - In the orientable category, we show that, if a finite group G acts on a closed surface Σ so that each element of it is extendable over the 3-sphere S3as a diffeomorphism with respect to a fixed embedding Σ → S3, then G is extendable over S3as a group action with respect to some other embedding Σ → S3. Degree one maps are involved in the proof.

AB - In the orientable category, we show that, if a finite group G acts on a closed surface Σ so that each element of it is extendable over the 3-sphere S3as a diffeomorphism with respect to a fixed embedding Σ → S3, then G is extendable over S3as a group action with respect to some other embedding Σ → S3. Degree one maps are involved in the proof.

UR - https://www.scopus.com/pages/publications/85208679193

U2 - 10.4310/CAG.241015032653

DO - 10.4310/CAG.241015032653

M3 - 文章

AN - SCOPUS:85208679193

SN - 1019-8385

VL - 32

SP - 889

EP - 921

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 3

ER -

Extending periodic automorphisms of surfaces to 3-manifolds

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