TY - JOUR
T1 - EXTENDING AUTOMORPHISMS of the GENUS-2 SURFACE over the 3-SPHERE
AU - Funayoshi, Kenta
AU - Koda, Yuya
N1 - Funding Information:
The second author is supported by JSPS KAKENHI Grant Numbers 15H03620, 17K05254, 17H06463, and JST CREST Grant Number JPMJCR17J4.
Publisher Copyright:
© 2019 The Author(s) 2019. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals. permissions@oup.com.
PY - 2020/3/13
Y1 - 2020/3/13
N2 - 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.
AB - 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.
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U2 - 10.1093/qmathj/haz042
DO - 10.1093/qmathj/haz042
M3 - Article
AN - SCOPUS:85084073176
SN - 0033-5606
VL - 71
SP - 175
EP - 196
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1
ER -