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Extendable periodic
automorphisms of closed surfaces over the $3$–sphere
Chao Wang and Weibiao Wang |
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Algebraic & Geometric Topology 24 (2024) 3327–3362
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Abstract |
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A periodic automorphism of a surface is said to be extendable over if it extends to a periodic automorphism of the pair for some possible embedding . We classify and construct all extendable automorphisms of closed surfaces, with orientation-reversing cases included. Moreover, they can all be induced by automorphisms of on Heegaard surfaces. As a byproduct, the embeddings of surfaces into lens spaces are discussed. |
Keywords
extendable map, cyclic group action, periodic surface map,
symmetry of 3–sphere
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Mathematical Subject Classification
Primary: 57M60, 57S17, 57S25
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References |
Publication
Received: 1 June 2021
Revised: 2 June 2022
Accepted: 5 January 2023
Published: 7 October 2024
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Authors |
| Chao Wang | |
| School of Mathematical Sciences
& Shanghai Key Laboratory of PMMP East China Normal University Shanghai China |
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| Weibiao Wang | |
| School of Mathematical
Sciences Peking University Beijing China |
School of Mathematics and
Statistics Central South University Changsha China |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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