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Connected sums of manifolds which induce approximate fibrations
Author(s):
Yongkuk
Kim
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1497-1506.
MSC (1991):
Primary 57N15, 55M25;
Secondary 57M10, 54B15
Posted:
February 3, 2000
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Abstract:
Codimension-2 fibrators are  -manifolds which automatically induce approximate fibration, in the following sense: given any proper mapping  from an  -manifold onto a  -manifold such that each point-preimage is a copy of the codimension-2 fibrator,  is necessarily an approximate fibration. In this paper, we give some answers to the following question: given an  -manifold  which is a nontrivial connected sum, when is  a codimension-2 fibrator?
References:
- 1.
- N. Chinen, Manifolds with nonzero Euler characteristic and codimension-2 fibrators, Topology Appl. 86 (1998) 151-167 MR 99c:57052
- 2.
- D.S. Coram and P.F. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977) 275-288 MR 56:1296
- 3.
- D.S. Coram and P.F. Duvall, Approximate fibrations and a movability condition for maps, Pacific J. Math. 72 ( 1977) 41-56 MR 57:7597
- 4.
- D.S. Coram and P.F. Duvall, Mappings from
 to  whose point inverses have the shape of a circle, General Topology Appl. 10 (1979) 239-246 MR 81b:57009 - 5.
- R.J. Daverman, Submanifold decompositions that induce approximate fibrations, Topology Appl. 33 (1989) 173-184 MR 91d:57013
- 6.
- R.J. Daverman, Hyperhopfian groups and approximate fibrations, Compositio Math. 86 (1993) 159-176 MR 94b:55022
- 7.
- R.J. Daverman, Codimension-2 fibrators with finite fundamental groups, Proc. Amer. Math. Soc. 127 (1999) 881-888 CMP 99:06
- 8.
- R.J. Daverman, 3-manifolds with geometric structure and approximate fibrations, Indiana Univ. Math. J. 40 (1991) 1451-1469 MR 92m:55016
- 9.
- R.J. Daverman, Manifolds with finite first homology as codimension 2 fibrators, Proc. Amer. Math. Soc. 113 (1991) 471-477 MR 92a:55015
- 10.
- R.J. Daverman and L.S. Husch, Decompositions and approximate fibrations, Michigan Math. J. 31 (1984) 197-214 MR 86a:54009
- 11.
- I.M.S. Dey and H. Neumann, The Hopf property of free products, Math. Z. 117 (1970) 325-339 MR 43:2099
- 12.
- B. Eckmann, Covering and Betti numbers, Bull. Amer. Math. Soc. 55 (1949) 95-101 MR 10:559a
- 13.
- J.C. Hausmann, Geometric hopfian and nonhopfian situations, Lecture Notes in Pure Appl. Math. Marcel Decker, Inc., NY (1987) 157-166 MR 88f:57031
- 14.
- Y. H. Im, Products of surfaces that induce approximate fibrations, Houston J. Math. 21 no. 2 (1995) 339-348 MR 96c:57038
- 15.
- Y. H. Im and Y. Kim, Hopfian and strongly hopfian manifolds, Fund. Math. 159 (1999), no. 2 127-134. MR 99j:57023
- 16.
- Y. Kim, Strongly hopfian manifolds as codimension-2 fibrators, Topology Appl. 92 (1999), no. 3 237-245. CMP 99:09
- 17.
- Y. Kim, Manifolds with hyperhopfian fundamental group as codimension-2 fibrators, Topology Appl. To appear
- 18.
- J. Milnor, Infinite cyclic coverings, in Conference on the Topology of Manifolds (J.G. Hocking ed.), Prindle Weber & Schmidt, Inc., Boston, 1968, 115-133 MR 39:3497
- 19.
- J.R. Munkres, Elements of Algebraic Topology, Addison Wesley Publ. Co., NY, 1984 MR 85m:55001
- 20.
- J. Roitberg, Residually finite, hopfian and co-hopfian spaces, Contemporary mathematics 37 (1985) 131-144 MR 86i:55009
- 21.
- J. J. Rotman, An Introduction to the Theory of Groups, Springer-Verlag, 1995. MR 95m:20001
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Additional Information:
Yongkuk
Kim
Affiliation:
Department of Mathematics, The University of Tennessee at Knoxville, Knoxville, Tennessee 37996-130
Address at time of publication:
Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea
Email:
yongkuk@kyungpook.ac.kr
DOI:
10.1090/S0002-9939-00-05385-5
PII:
S 0002-9939(00)05385-5
Keywords:
Connected sum,
approximate fibration,
codimension-2 fibrator,
hopfian manifold,
hyperhopfian group,
residually finite group
Received by editor(s):
February 12, 1998
Posted:
February 3, 2000
Communicated by:
Ralph Cohen
Copyright of article:
Copyright
2000,
American Mathematical Society
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