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 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