On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds

Hass, Joel; Wang, Shicheng; Zhou, Qing

doi:10.1090/S0002-9939-01-06262-1

On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds

Authors: Joel Hass, Shicheng Wang and Qing Zhou
Journal: Proc. Amer. Math. Soc. 130 (2002), 1851-1857
MSC (1991): Primary 57N10; Secondary 57M50, 53A10
DOI: https://doi.org/10.1090/S0002-9939-01-06262-1
Published electronically: October 23, 2001
MathSciNet review: 1887034
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Abstract | References | Similar Articles | Additional Information

Abstract: For any hyperbolic 3-manifold with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of $\partial M$ is bounded from above.

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Additional Information

Joel Hass
Affiliation: Department of Mathematics, University of California, Davis, California 95616
Email: hass@math.ucdavis.edu

Shicheng Wang
Affiliation: Department of Mathematics, Peking University, Beijing 100871, People’s Republic of China
Email: swang@sxx0.math.pku.edu.cn

Qing Zhou
Affiliation: Department of Mathematics, East China Normal University, Shanghai, 200062, People’s Republic of China
Email: qzhou@euler.math.ecnu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-01-06262-1
Keywords: Boundary slopes, three-dimensional topology, essential surfaces
Received by editor(s): September 2, 1999
Received by editor(s) in revised form: December 28, 2000
Published electronically: October 23, 2001
Additional Notes: The first author was partially supported by NSF grant DMS-9704286.
The second and third authors were partially supported by MSTC and Outstanding Youth Fellowships of NSFC
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society