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March 2019 Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic $3$-manifolds
Yi Liu
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J. Differential Geom. 111(3): 457-493 (March 2019). DOI: 10.4310/jdg/1552442607

Abstract

In this paper, it is shown that every closed hyperbolic $3$-manifold contains an immersed quasi-Fuchsian closed subsurface of odd Euler characteristic. The construction adopts the good pants method, and the primary new ingredient is an enhanced version of the connection principle, which allows one to connect any two frames with a path of frames in a prescribed relative homology class of the frame bundle. The existence result is applied to show that every uniform lattice of $\mathrm{PSL}(2, \mathbb{C})$ admits an exhausting nested sequence of sublattices with exponential homological torsion growth. However, the constructed sublattices are not normal in general.

Funding Statement

The author was supported by the Recruitment Program of Global Youth Experts of China.

Citation

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Yi Liu. "Immersing quasi-Fuchsian surfaces of odd Euler characteristic in closed hyperbolic $3$-manifolds." J. Differential Geom. 111 (3) 457 - 493, March 2019. https://doi.org/10.4310/jdg/1552442607

Information

Received: 2 August 2016; Published: March 2019
First available in Project Euclid: 13 March 2019

zbMATH: 07036513
MathSciNet: MR3934597
Digital Object Identifier: 10.4310/jdg/1552442607

Subjects:
Primary: 57M50
Secondary: 30F40, 57M10

Rights: Copyright © 2019 Lehigh University

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Vol.111 • No. 3 • March 2019
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