Necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators

Authors:
Young Ho Im and Yongkuk Kim

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2135-2140

MSC (2000):
Primary 57N15, 55M25; Secondary 57M10, 54B15

DOI:
https://doi.org/10.1090/S0002-9939-00-05998-0

Published electronically:
December 13, 2000

MathSciNet review:
1825927

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Fibrators help detect approximate fibrations. A closed, connected -manifold is called a codimension-2 fibrator if each map defined on an -manifold such that all fibre , are shape equivalent to is an approximate fibration. The most natural objects to study are s-Hopfian manifolds. In this note we give some necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators.

**1.**N. Chinen, Finite groups and approximate fibrations,*Topology Appl.***102**(2000) 59-88 CMP**2000:08****2.**S.E. Cappell and J.L. Shaneson, Some new four-manifolds,*Ann. of Math. (2)***104**(1976) 61-72 MR**54:6167****3.**D.S. Coram and P.F. Duvall, Approximate fibration,*Rocky Mountain J. Math.***7**(1977) 275-288 MR**56:1296****4.**D.S. Coram and P.F. Duvall, Approximate fibration and a movability condition for maps,*Pacific J. Math.***72**(1977) 41-56 MR**57:7597****5.**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****6.**R.J. Daverman, Submanifold decompositions that induce approximate fibrations,*Topology Appl.***33**(1989) 173-184 MR**91d:57013****7.**R.J. Daverman, Hyper-Hopfian groups and approximate fibrations,*Compositio Math.***86**(1993) 159-176 MR**94b:55022****8.**R.J. Daverman, Codimension-2 fibrators with finite fundamental groups,*Proc. Amer. Math. Soc.***127**(1999) 881-888 MR**2000a:57051****9.**R.J. Daverman and Y. Kim, 2-groups and approximate fibrations,*Topology Appl.*To appear**10.**R.J. Daverman, Y.H. Im and Y. Kim, Products of Hopfian manifolds and codimension-2 fibrators,*Topology Appl.***103**(2000) 323-338 CMP**2000:12****11.**R. Fintushel and R.J. Stern, Smooth free involutions on homotopy -spheres,*Michigan Math. J.***30**(1983) 37-51 MR**84f:57025****12.**J.A. Hillman,*The algebraic characterization of geometric**-manifolds*, Cambridge Univ. Press, Cambridge, 1994 MR**95m:57032****13.**J.A. Hillman,*-knots and their groups*, Cambridge Univ. Press, Cambridge, 1989 MR**90d:57025****14.**R. Hirshon, Some properties of endomorphisms in residually finite groups,*J. Austral. Math. Soc.**Series A***34**(1977), 117-120. MR**57:9847****15.**Y.H. Im and Y. Kim, Hopfian and strongly hopfian manifolds,*Fund. Math.***159**(1999) 127-134 MR**99j:57023****16.**Y. Kim, Strongly Hopfian manifolds as codimension-2 fibrators.*Topology Appl.***92**(1999) 237-245 MR**2000g:57036****17.**Y. Kim, Connected sums of manifolds which induce approximate fibrations,*Proc. Amer. Math. Soc.***128**(2000) 1497-1506 MR**2000j:57052****18.**Y. Kim, Manifolds with hyper-Hopfian fundamental group as codimension-2 fibrators,*Topology Appl.***96**(1999) 241-248 CMP**2000:01****19.**S. Lopez de Medrano,*Involutions on manifolds*, Springer-Verlag, New York, (1971) MR**45:7747**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
57N15,
55M25,
57M10,
54B15

Retrieve articles in all journals with MSC (2000): 57N15, 55M25, 57M10, 54B15

Additional Information

**Young Ho Im**

Affiliation:
Department of Mathematics, Pusan National University, Pusan, 609-735, Korea

Email:
yhim@hyowon.pusan.ac.kr

**Yongkuk Kim**

Affiliation:
Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea

Email:
yongkuk@knu.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-00-05998-0

Keywords:
Codimension-2 fibrator,
s-Hopfian manifold,
Hopfian group,
approximate fibration

Received by editor(s):
October 19, 1999

Published electronically:
December 13, 2000

Additional Notes:
The first author’s research was supported by Korea Research Foundation Grant (KRF-2000-041-D00023)

The second author’s research was supported by Korea Research Foundation Grant (KRF-2000-015-DP0034)

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 2000
American Mathematical Society