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

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Category Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 962))

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References

  1. M.A. Armstrong, On the fundamental group of an orbit space, Proc. Cambridge Philos. Soc. 61 (1965) 639–646.

    Article  MathSciNet  MATH  Google Scholar 

  2. M.A. Armstrong, The fundamental group of the orbit space of a discontinuous group, Proc. Cambridge Philos. Soc. 64 (1968) 299–301.

    Article  MathSciNet  MATH  Google Scholar 

  3. G.E. Bredon, Equivariant Cohomology Theories, Springer Lecture Notes in Math. 34 (1967).

    Google Scholar 

  4. R. Brown, Groupoids and van Kampen's theorem, Proc.London Math. Soc. (3) 17 (1967) 385–401.

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Brown, Fibrations of groupoids, J.Algebra 15 (1970) 103–132.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Brown and P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981) 233–260.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Brown and P.J. Higgins, Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981) 11–41.

    Article  MathSciNet  MATH  Google Scholar 

  8. R.Brown and P.J.Higgins, Crossed complexes and non-abelian extensions, this volume.

    Google Scholar 

  9. P.J. Higgins, Notes on Categories and Groupoids, Van Nostrand Mathematical Studies 32 (1971).

    Google Scholar 

  10. F. Rhodes, On the fundamental group of a transformation group, Proc.London Math. Soc. (3) 16 (1966) 635–650.

    Article  MathSciNet  MATH  Google Scholar 

  11. E.H. Spanier, Algebraic Topology, McGraw-Hill Series in Higher Mathematics (1966).

    Google Scholar 

  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 

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Klaus Heiner Kamps Dieter Pumplün Walter Tholen

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© 1982 Springer-Verlag

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Higgins, P.J., Taylor, J. (1982). The fundamental groupoid and the homotopy crossed complex of an orbit space. In: Kamps, K.H., Pumplün, D., Tholen, W. (eds) Category Theory. Lecture Notes in Mathematics, vol 962. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066890

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  • DOI: https://doi.org/10.1007/BFb0066890

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11961-6

  • Online ISBN: 978-3-540-39550-8

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