The fundamental groupoid and the homotopy crossed complex of an orbit space

  • P. J. Higgins
  • J. Taylor
Conference paper
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 962)

Keywords

Fundamental Group Simplicial Complex Orbit Space Vertex Group Canonical Morphism 
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References

  1. 1.
    M.A. Armstrong, On the fundamental group of an orbit space, Proc. Cambridge Philos. Soc. 61 (1965) 639–646.MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    M.A. Armstrong, The fundamental group of the orbit space of a discontinuous group, Proc. Cambridge Philos. Soc. 64 (1968) 299–301.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    G.E. Bredon, Equivariant Cohomology Theories, Springer Lecture Notes in Math. 34 (1967).Google Scholar
  4. 4.
    R. Brown, Groupoids and van Kampen's theorem, Proc.London Math. Soc. (3) 17 (1967) 385–401.MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    R. Brown, Fibrations of groupoids, J.Algebra 15 (1970) 103–132.MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    R. Brown and P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981) 233–260.MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    R. Brown and P.J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981) 11–41.MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    R.Brown and P.J.Higgins, Crossed complexes and non-abelian extensions, this volume.Google Scholar
  9. 9.
    P.J. Higgins, Notes on Categories and Groupoids, Van Nostrand Mathematical Studies 32 (1971).Google Scholar
  10. 10.
    F. Rhodes, On the fundamental group of a transformation group, Proc.London Math. Soc. (3) 16 (1966) 635–650.MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    E.H. Spanier, Algebraic Topology, McGraw-Hill Series in Higher Mathematics (1966).Google Scholar
  12. 12.
    J.Taylor, Group actions on ω-groupoids and crossed complexes and the homotopy groups of orbit spaces, Ph.D. thesis, Univ. of Durham (1982).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • P. J. Higgins
    • 1
  • J. Taylor
    • 1
  1. 1.Department of MathematicsUniversity of Durham, Science LaboratoriesDurhamUK

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