Homology-genericity, horizontal Dehn surgeries and ubiquity of rational homology 3-spheres

Author:
Jiming Ma

Journal:
Proc. Amer. Math. Soc. **140** (2012), 4027-4034

MSC (2010):
Primary 57M27, 57M99

Published electronically:
March 7, 2012

MathSciNet review:
2944742

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show that rational homology 3-spheres are ubiquitous from the viewpoint of Heegaard splitting. Let be a genus Heegaard splitting of a closed -manifold and be a simple closed curve in . Then there is a 3-manifold which is obtained from by horizontal Dehn surgery along . We show that for such that the homology class is generic in the set of curve-represented homology classes , }. As a corollary, for a set of curves , , such that each is generic in , is a rational homology 3-sphere.

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Additional Information

**Jiming Ma**

Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, People’s Republic of China 200433

Email:
majiming@fudan.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11224-9

Keywords:
Rational homology 3-sphere,
Heegaard splitting,
homology-genericity.

Received by editor(s):
January 31, 2010

Received by editor(s) in revised form:
June 3, 2010, September 17, 2010, March 4, 2011, and April 26, 2011

Published electronically:
March 7, 2012

Additional Notes:
The author was supported in part by RFDP 200802461001 and NSFC 10901038.

Communicated by:
Daniel Ruberman

Article copyright:
© Copyright 2012
American Mathematical Society