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Branched coverings and nonzero degree maps between Seifert manifolds
Author(s):
Hong
Huang
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2443-2449.
MSC (2000):
Primary 57N10;
Secondary 57M12, 55M25
Posted:
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  ). 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.
References:
-
- 1.
- A. Casson, D. Jungreis, Convergence groups and Seifert fibered 3-manifolds, Invent. Math. 118 (1994), 441-456. MR 96f:57011
- 2.
- A. L. Edmonds, R. S. Kulkarni and R. E. Stong, Realizability of branched coverings of surfaces, Trans. Amer. Math. Soc. 282 (1984), No. 2, 773-790. MR 85k:57005
- 3.
- D. Gabai, Convergence groups are Fuchisian groups. Ann. of Math. 136 (1992), 447-510. MR 93m:20065
- 4.
- D. Husemoller, Ramified coverings of Riemann surfaces, Duke Math. J. 29 (1962), 167-174. MR 25:188
- 5.
- W. Jaco, P. Shalen, Seifert Fibered Spaces in 3-manifolds, Memoirs of Amer. Math. Soc. 21 (1979) (no. 220). MR 81c:57010
- 6.
- W. D. Neumann, F. Raymond, Seifert manifolds, plumbing,
 -invariant and orientation reversing maps, Lecture Notes in Mathematics 664, 162-195. MR 80e:57008 - 7.
- Y. Rong, Maps between Seifert fibered spaces of infinite
 , Pacific J. Math. 160 (1993), No. 1, 143-154. MR 94e:55026 - 8.
- Y. Rong, Degree one maps of Seifert manifolds and a note on Seifert volume, Topol. Appl. 64 (1995), 191-200. MR 96c:57034
- 9.
- P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487. MR 84m:57009
- 10.
- H. Seifert, Topologie dreidimensionaler gefaserter Raume, Acta Math. 60 (1933), 147-238.
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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:
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
Posted:
February 4, 2002
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2002,
American Mathematical Society
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