|
Any 3-manifold 1-dominates at most finitely many 3-manifolds of  -geometry
Author(s):
Claude
Hayat-Legrand;
Shicheng
Wang;
Heiner
Zieschang
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3117-3123.
MSC (2000):
Primary 55M25, 54C05, 57M05
Posted:
March 14, 2002
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Any 3-manifold 1-dominates at most finitely many 3-manifolds supporting  geometry.
References:
-
- 1.
- Boileau M. and Wang S.C. Nonzero degree maps and surface bundles over
 , J. Diff. Geom. 43 (1996), 789-908. MR 98g:57023 - 2.
- Browder, W.: Surgery on simply-connected manifolds. Berlin-Heidelberg-New York: Springer 1972. MR 50:11272
- 3.
- Kirby, R.: Problems in low-dimensional topology. Geometric topology, Edited by H. Kazez, AMS/IP Vol. 2., International Press, 1997. MR 98f:57001
- 4.
- Hayat-Legrand, C.; Wang, S.C. and Zieschang, H.: Degree one maps onto Lens Spaces. Pacific J. Math. 176, 19-32 (1996) MR 98b:57030
- 5.
- Munkres, J., Elements of Algebraic Topology. Addison-Wesley Publish Company 1984. MR 85m:55001
- 6.
- Neumann, W.D. and Raymond, F., Seifert manifolds, plumbing,
 -invariant and orientation reversing maps, Lect. Note in Math. 664, 162-195, Springer, 1978. MR 80e:57008 - 7.
- Reid, A. and Wang, S.C., Non-Haken 3-manifolds is not larger with respect to mappings of nonzero degree, Comm. Analy. Geom. Vol. 7, No. 1, 105-132 (1999). MR 2000c:57042
- 8.
- Rong, Y. Degree one maps between geometric
 -manifolds. Trans. Amer. Math Soc, 322 411-436 (1992). MR 92j:57007 - 9.
- Rong, Y. Maps between Seifert fibered spaces of infinite
 . Pacific J. Math. 160, 143-154 (1993). MR 94e:55026 - 10.
- Rong, Y. Degree one maps of Seifert manifolds and a note on Seifert volume, Topology and its Application. Vol. 64 No. 2 191-200 (1995). MR 96c:57034
- 11.
- Scott, G.P., The geometries of
 -manifolds. Bull. London Math. Soc. 15, 401-487 (1983). - 12.
- Seifert, H. and Threlfall, W., A text book of topology (English transl.) Academic Press 1980. MR 82b:55001
- 13.
- Soma, T., Nonzero degree maps to hyperbolic 3-manifolds, J. Diff. Geom. 49 (1998), 517-546. MR 2000b:57034
- 14.
- Soma, T., Sequences of degree-one maps between geometric 3-manifolds, Math. Annalen. 316, (2000) 733-742. MR 2001b:57039
- 15.
- Spanier, E., Algebraic Topology. McGraw-Hill Book Comp., New York, N.Y. 1966. MR 35:1007
- 16.
- Wang, S.C. and Zhou, Q., Any
 -manifold  -dominates only finitely Seifert manifolds with infinite  . Math. Annalen, in press.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
55M25, 54C05, 57M05
Retrieve articles in all Journals with MSC
(2000):
55M25, 54C05, 57M05
Additional Information:
Claude
Hayat-Legrand
Affiliation:
Department of Mathematics, University of Sabatier, Toulouse 31062, France
Email:
hayat@picard.ups-tlse.fr
Shicheng
Wang
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
Email:
wangsc@math.pku.edu.cn
Heiner
Zieschang
Affiliation:
Department of Mathematics, Ruhr University, Bochum 44780, Germany
Email:
marlene.schwarz@rz.ruhr-uni-bochum.de
DOI:
10.1090/S0002-9939-02-06438-9
PII:
S 0002-9939(02)06438-9
Keywords:
3-manifold,
degree one map
Received by editor(s):
November 17, 2000
Received by editor(s) in revised form:
May 23, 2001
Posted:
March 14, 2002
Additional Notes:
The second author was partially supported by MSTC and Outstanding Youth Fellowships of NSFC
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org