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Extendable periodic automorphisms of closed surfaces over the 3-sphere (2111.06542v1)

Published 12 Nov 2021 in math.GT

Abstract: A periodic automorphism of a surface $\Sigma$ is said to be extendable over $S3$ if it extends to a periodic automorphism of the pair $(S3,\Sigma)$ for some possible embedding $\Sigma\to S3$. 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 by-product, the embeddings of surfaces into lens spaces are discussed.

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