Skip to main content
SpringerLink
Log in

Five dimensional Bieberbach groups with trivial centre

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Let Γ be a Bieberbach group—that is a torsion free crystallographic group. In this paper is given a list of the isomorphy types of all holonomy groups of five-dimensional Bieberbach groups with trivial centre.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Brown, R. Bülow, J. Neubüser, H. Wondratschek, H. Zassenhaus: Crystallographic groups of four-dimensional space. New York, Wiley, 1978

    MATH  Google Scholar 

  2. L.S. Charlap: Bieberbach groups and flat manifolds. Springer Verlag 1986

  3. P. Cobb: Manifolds with holonomyZ 2×Z 2 and first Betti number zero. Jour. Diff. Geom. 10(1975) 221–224

    MATH  MathSciNet  Google Scholar 

  4. F.T. Farrell, W.C. Hsiang: The toplogical-euclidean space form problem. Invent. math. 45(1978) 181–192

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Gorenstein: Finite Groups. Harper & Row Publishers 1968

  6. M. Hall Jr., J.K. Senior: The group of order 2n (n≤6). The Macmillan company, 1964

  7. H. Hiller, C.H. Sah: Holonomy of flat manifolds withb 1=0. Q. J. Math. Oxf. II Ser. 37(1986) 177–187

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Hiller, Z. Marciniak, C.H. Sah, A. Szczepański: Holonomy of flat manifolds withb 1=0 II. Q. J. Math. Oxf. II Ser. 38 (1987) 213–220

    Article  MATH  Google Scholar 

  9. S. Maclane: Homology. Springer Verlag 1963

  10. Z. Marciniak, A. Szczepański: Extensions of Crystallographic groups. preprint 1988

  11. J. Neubüser: Classification of groups of order ≤100. preprint Kiel 1967.

  12. P.A. Symonds: Flat manifolds. Ph.D. Thesis, 1987 Cambridge University

  13. A. Szczepański: Euclidean space forms with the first Betti number aqual to zero. Q. J. Math. Oxf. II Ser 36 (1985) 489–493

    Article  Google Scholar 

  14. A.D. Thomas, G.V. Wood: Group tables. Shiva Publishing Limitid 1980.

Download references

Author information

Author notes

  1. Andrzej Szczepański

    Present address: Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, ul. Majakowskiego 11/12, 80-952, Gdańsk, Poland

Authors and Affiliations

  1. Lehrstuhl B für Mathematik, RWTH Aachen, Templergraben 64, D-5100, Aachen, West Germany

    Andrzej Szczepański

Authors
  1. Andrzej Szczepański
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Szczepański, A. Five dimensional Bieberbach groups with trivial centre. Manuscripta Math 68, 191–208 (1990). https://doi.org/10.1007/BF02568759

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568759

Keywords

Search

Navigation