Bull. Korean Math. Soc. 2022; 59(2): 351-360
Online first article March 31, 2022 Printed March 31, 2022
https://doi.org/10.4134/BKMS.b210150
Copyright © The Korean Mathematical Society.
Konkuk University
We prove that a punctured-torus group of hyperbolic $4$-space which keeps an embedded hyperbolic $2$-plane invariant has a strictly parabolic commutator. More generally, this rigidity persists for a punctured-surface group.
Keywords: Hyperbolic geometry, hyperbolic $4$-space, parabolic isometry, punctured-surface group, punctured-torus group, deformation, rigidity
MSC numbers: Primary 57M50, 51M09; Secondary 30F40, 22E40
Supported by: This paper was supported by Konkuk University in 2018.
2020; 57(6): 1367-1382
2019; 56(5): 1341-1353
2017; 54(6): 2119-2139
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