Advertisement

Examples of lack of rigidity in crystallographic groups

Geometry Of Manifolds
Part of the Lecture Notes in Mathematics book series (LNM, volume 1474)

Keywords

Spectral Sequence Holonomy Group Crystallographic Group Grothendieck Ring Whitehead Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [B]
    Bass, H.:Algebraic K-Theory. New York: W.A.Benjamin Inc., 1968zbMATHGoogle Scholar
  2. [BM]
    Bass, H., Murthy, P.: Grothendieck groups and Picard groups of Abelian group rings. Annals of Math.(2)86,16–73 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  3. [C]
    Carter, D.: Lower K-theory of finite groups. Comm. Algebra 8 1927–1937 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  4. [CdaS]
    Connolly, F., daSilva, M.:N i K 0(Zπ) is a finitely generated ZN i module for any finite group π. (to appear)Google Scholar
  5. [CK1]
    Connolly, F., Koźniewski, T.: Finiteness properties of classifying spaces of proper Γ actions. Journal of Pure and Applied Algebra 41, 17–36 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  6. [CK2]
    Connolly, F., Koźniewski, T.:Rigidity and Crystallographic Groups, I. Inventiones Math.99 25–49 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  7. [CK3]
    Connolly, F., Koźniewski, T.:Rigidity and Crystallographic Groups, II. (in preparation)Google Scholar
  8. [CL]
    Connolly, F., Lück, W.: The involution on the Equivariant Whitehead Group. Journal of K-Theory,(to appear, 1990)Google Scholar
  9. [F]
    Farrell, F.T.:The obstruction to fibering a manifold over a circle. Indiana Univ. Math. J. 21,3125–346 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  10. [FH1]
    Farrell, F.T., Hsiang, W.C.: A formula for K 1(R α[T]). Proc. Symp. Pure Math. vol. 17 (1970)Google Scholar
  11. [FH2]
    Farrell, F.T., Hsiang, W.C.: Topological Characterization of flat and almost flat manifolds, M n, n ≠ 3, 4. Amer. Jour. Math.105,641–672 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  12. [HS]
    Hsiang, W.C., Shaneson, J.: Fake Tori. In: Topology of Manifolds. Chicago, Markham 1970 pp. 18–51Google Scholar
  13. [M]
    Milnor, J.W.: Whitehead Torsion. Bulletin of the Amer. Math. Soc. 72, 358–426 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  14. [Q1]
    Quinn, F.: Ends of maps II. Inventiones Math.68,353–424 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [Q2]
    Quinn, F.: Algebraic K-theory of poly-(finite or cyclic) groups, Bulletin of the Amer. Math. Soc. 12, 221–226 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  16. [St]
    Steinberger, M.: The equivariant topological s-cobordism theorem. Inventiones Math. 91, 61–104 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  17. [StW]
    Steinberger, M., West, J.:Equivariant h-cobordisms and finiteness obstructions. Bulletin of the Amer. Math. Soc. 12, 217–220 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  18. [Sw]
    Swan, R.: The Grothendieck ring of a finite group. Topology 2, 85–110 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  19. [Ts]
    Tsapogas, G.: On the K-theory of crystallographic groups, Ph.D. dissertation, University of Notre Dame, 1990.Google Scholar
  20. [W]
    Weinberger, S.: Private communicationGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Instytut MatematykiWarsaw UniversityWarszawaPoland

Personalised recommendations