Proceedings of the American Mathematical Society

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

Author(s): Joel Hass; Shicheng Wang; Qing Zhou
Journal: Proc. Amer. Math. Soc. 130 (2002), 1851-1857.
MSC (1991): Primary 57N10; Secondary 57M50, 53A10
Posted: October 23, 2001
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57N10, 57M50, 53A10

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: 10.1090/S0002-9939-01-06262-1
PII: S 0002-9939(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
Posted: 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
Copyright of article: Copyright 2001, American Mathematical Society

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