Extendable periodic automorphisms of closed surfaces over the 3–sphere

Chao Wang; Weibiao Wang

doi:10.2140/agt.2024.24.3327

Extendable periodic automorphisms of closed surfaces over the 3–sphere

Chao Wang
, Weibiao Wang

School of Mathematical Sciences

Peking University

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

2 Scopus citations

Abstract

A periodic automorphism of a surface † is said to be extendable over S³ if it extends to a periodic automorphism of the pair.†; S³/ for some possible embedding †,! S³. We classify and construct all extendable automorphisms of closed surfaces, with orientation-reversing cases included. Moreover, they can all be induced by automorphisms of S³ on Heegaard surfaces. As a byproduct, the embeddings of surfaces into lens spaces are discussed.

Original language	English
Pages (from-to)	3327-3362
Number of pages	36
Journal	Algebraic and Geometric Topology
Volume	24
Issue number	6
DOIs	https://doi.org/10.2140/agt.2024.24.3327
State	Published - 2024

Keywords

cyclic group action
extendable map
periodic surface map
symmetry of 3–sphere

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abstract = "A periodic automorphism of a surface † is said to be extendable over S3 if it extends to a periodic automorphism of the pair.†; S3/ for some possible embedding †,! S3. We classify and construct all extendable automorphisms of closed surfaces, with orientation-reversing cases included. Moreover, they can all be induced by automorphisms of S3 on Heegaard surfaces. As a byproduct, the embeddings of surfaces into lens spaces are discussed.",

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AB - A periodic automorphism of a surface † is said to be extendable over S3 if it extends to a periodic automorphism of the pair.†; S3/ for some possible embedding †,! S3. We classify and construct all extendable automorphisms of closed surfaces, with orientation-reversing cases included. Moreover, they can all be induced by automorphisms of S3 on Heegaard surfaces. As a byproduct, the embeddings of surfaces into lens spaces are discussed.

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KW - extendable map

KW - periodic surface map

KW - symmetry of 3–sphere

UR - https://www.scopus.com/pages/publications/85207829544

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M3 - 文章

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ER -

Extendable periodic automorphisms of closed surfaces over the 3–sphere

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Keywords

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