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Group extensions are quasi-simply-filtrated

Published online by Cambridge University Press:  17 April 2009

S.G. Brick  and
M.L. Mihalik
S.G. Brick
Affiliation:
Department of Mathematics CSU-Fresno Fresno CA 93740United States of America e-mail: stephen@zimmer.csufresno.edu
M.L. Mihalik
Affiliation:
Department of MathematicsVanderbilt University NashvilleTN 37240United States of America e-mail: mihalikm@ctrvax.vanderbilt.edu
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Abstract

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A finitely presented group G is quasi-simply-filtrated (abbreviated qsf) if, given a finite complex with fundamental group G, the universal cover of the complex can be “approximated” by simply connected finite complexes. This notion is a generalisation of a concept of Casson's used in the study of three-manifolds.

In this paper we show that any extension of a finitely presented infinite group by a finitely presented infinite group is qsf.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 21 - 27
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Brick, S.G., ‘Quasi-isometries and ends of groups’, J. Pure Appl. Algebra (to appear).Google Scholar
[2]Brick, S.G. and Mihalik, M.L., ‘Qsf property for groups and spaces’, (preprint).Google Scholar
[3]Gersten, S.M. and Stallings, J.R., ‘Casson's idea about 3-manifolds whose universal cover is ℝ3’, Internat. J. of Algebra and Comput. 1 (1991), 395–406.Google Scholar
[4]Mihalik, M.L. and Tschantz, S.T., ‘Tame combings and the quasi-simply-filtered condition for groups’, (preprint).Google Scholar
[5]Stallings, J. R., ‘Brick's quasi simple nitrations for groups and 3-manifolds’, in Geometric methods in group theory, University of Sussex, July, 1991 (to appear).Google Scholar