EXTENDING AUTOMORPHISMS of the GENUS-2 SURFACE over the 3-SPHERE

Kenta Funayoshi, Yuya Koda

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

An automorphism f of a closed orientable surface Σ is said to be extendable over the 3-sphere S3 if f extends to an automorphism of the pair (S3, Σ) with respect to some embedding Σ hookrightarrow S3. We prove that if an automorphism of a genus-2 surface Σ is extendable over S3, then f extends to an automorphism of the pair (S3, Σ) with respect to an embedding Σ hookrightarrow S3 such that Σ bounds genus-2 handlebodies on both sides. The classification of essential annuli in the exterior of genus-2 handlebodies embedded in S3 due to Ozawa, and the second author plays a key role.

Original languageEnglish
Pages (from-to)175-196
Number of pages22
JournalQuarterly Journal of Mathematics
Volume71
Issue number1
DOIs
Publication statusPublished - 2020 Mar 13
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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