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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Branched coverings and nonzero degree maps between Seifert manifolds


Author: Hong Huang
Journal: Proc. Amer. Math. Soc. 130 (2002), 2443-2449
MSC (2000): Primary 57N10; Secondary 57M12, 55M25
Published electronically: February 4, 2002
MathSciNet review: 1897471
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Abstract: In this note we give a necessary and sufficient condition for the existence of a fiber preserving branched covering between two closed, orientable Seifert manifolds (for sufficiency we need the additional assumption that the genus of the base orbifold of the target manifold $\geq 1$). Combining this with two theorems of Rong we get a necessary and sufficient condition for the existence of a nonzero degree map between two such manifolds.


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Additional Information

Hong Huang
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Address at time of publication: Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
Email: hhuang01@263.net

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06306-2
PII: S 0002-9939(02)06306-2
Keywords: Seifert manifold, branched covering, nonzero degree map
Received by editor(s): October 27, 2000
Received by editor(s) in revised form: February 21, 2001
Published electronically: February 4, 2002
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2002 American Mathematical Society