Reducible and -reducible handle additions

Authors:
Ruifeng Qiu and Mingxing Zhang

Journal:
Trans. Amer. Math. Soc. **361** (2009), 1867-1884

MSC (2000):
Primary 57M50

Published electronically:
November 24, 2008

MathSciNet review:
2465821

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a simple 3-manifold with a component of of genus at least two. For a slope on , we denote by the manifold obtained by attaching a 2-handle to along a regular neighborhood of on . Suppose that and are two separating slopes on such that and are reducible. Then the distance between and is at most 2. As a corollary, if , then there is at most one separating slope on such that is either reducible or -reducible.

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Additional Information

**Ruifeng Qiu**

Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian, People’s Republic of China, 116022

Email:
qiurf@dlut.edu.cn

**Mingxing Zhang**

Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian, People’s Republic of China, 116022

Email:
zhangmx@dlut.edu.cn

DOI:
https://doi.org/10.1090/S0002-9947-08-04761-2

Keywords:
Handle addition,
Scharlemann cycle,
virtual Scharlemann cycle

Received by editor(s):
March 4, 2007

Published electronically:
November 24, 2008

Additional Notes:
This research was supported by NSFC(10625102) and a grant of SRFDP

Article copyright:
© Copyright 2008
American Mathematical Society