TY - JOUR
T1 - Goeritz Groups of Bridge Decompositions
AU - Hirose, Susumu
AU - Iguchi, Daiki
AU - Kin, Eiko
AU - Koda, Yuya
N1 - Funding Information:
This work was supported by the Japan Society for the Promotion of Science: Grant-in-Aid for Scientific Research [JP16K05156 and JP20K03618 to S.H., JP18K03299 to E.K., JP17K05254, JP17H06463, and JP20K03588 to Y.K.]; and Japan Science and Technology Agency: CREST [JPMJCR17J4 to Y.K.].
Publisher Copyright:
© 2021 The Author(s).
PY - 2022/6/1
Y1 - 2022/6/1
N2 - For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. After describing basic properties of this group, we discuss the asymptotic behavior of the minimal pseudo-Anosov entropies. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings of the 3-sphere and the real projective space.
AB - For a bridge decomposition of a link in the 3-sphere, we define the Goeritz group to be the group of isotopy classes of orientation-preserving homeomorphisms of the 3-sphere that preserve each of the bridge sphere and link setwise. After describing basic properties of this group, we discuss the asymptotic behavior of the minimal pseudo-Anosov entropies. We then give an application to the asymptotic behavior of the minimal entropies for the original Goeritz groups of Heegaard splittings of the 3-sphere and the real projective space.
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U2 - 10.1093/imrn/rnab001
DO - 10.1093/imrn/rnab001
M3 - Article
AN - SCOPUS:85132847679
SN - 1073-7928
VL - 2022
SP - 9308
EP - 9356
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 12
ER -