Seifert manifolds with fiber

spherical space forms

Authors:
Jong Bum Lee, Kyung Bai Lee and Frank Raymond

Journal:
Trans. Amer. Math. Soc. **348** (1996), 3763-3798

MSC (1991):
Primary 57M50; Secondary 55R60, 57M05, 57M60

MathSciNet review:
1348866

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the Seifert fiber spaces modeled on the product space . Such spaces are ``fiber bundles'' with singularities. The regular fibers are spherical space-forms of , while singular fibers are finite quotients of regular fibers. For each of possible space-form groups of , we obtain a criterion for a group extension of to act on as weakly -equivariant maps, which gives rise to a Seifert fiber space modeled on with weakly -equivariant maps as the universal group. In the course of proving our main results, we also obtain an explicit formula for for a cocompact crystallographic or Fuchsian group . Most of our methods for apply to compact Lie groups with discrete center, and we state some of our results in this general context.

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Additional Information

**Jong Bum Lee**

Affiliation:
Department of Mathematics, Sogang University, Seoul 121–742, Korea

Email:
jlee@ccs.sogang.ac.kr

**Kyung Bai Lee**

Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019

Email:
kblee@.math.uoknor.edu

**Frank Raymond**

Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Email:
fraymond@math.lsa.umich.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-96-01609-1

Keywords:
Seifert fiber space,
spherical space-form,
Fuchsian group,
crystallographic group,
group extension,
cohomology of groups

Received by editor(s):
December 1, 1994

Received by editor(s) in revised form:
September 7, 1995

Additional Notes:
The first author was supported in part by the Basic Science Research Institute Program, Ministry of Education, 1994, Project No. BSRI-94-1422, and by TGRC-KOSEF, Korea.

The third author was supported in part by National Science Foundation grant DMS-9306240, U.S.A

Article copyright:
© Copyright 1996
American Mathematical Society