Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-02-06306-2
Published electronically: February 4, 2002
MathSciNet review: 1897471
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 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, $\mu$-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 $\pi_1$, 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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57N10, 57M12, 55M25

Retrieve articles in all journals with MSC (2000): 57N10, 57M12, 55M25


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: https://doi.org/10.1090/S0002-9939-02-06306-2
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

American Mathematical Society