Skip to main content
SpringerLink
Log in

Equivalent homotopy theories and groups of self-equivalences

  • Research Papers
  • Conference paper
  • First Online:
Groups of Self-Equivalences and Related Topics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1425))

  • 437 Accesses

This paper is in final form and no version of it will be submitted for publication elsewhere

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Bencivenga, On the groups of automorphisms of principal and fibre bundles, Ph.D. thesis, Memorial University of Newfoundland, March 1982.

    Google Scholar 

  2. P. Booth, Classifying spaces for a general theory of fibrations (to appear).

    Google Scholar 

  3. P. Booth, Maps between classifying spaces and the classification of fibrations (to appear).

    Google Scholar 

  4. P. Booth and R. Brown, On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps, Gen. Top. and its Applications 8 (1978) 165–179.

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Booth, P. Heath and R. Piccinini, Fibre preserving maps and functional spaces, Lecture notes in Math. 673 (Springer-Verlag, Berlin, 1978) 158–167.

    MATH  Google Scholar 

  6. P. Booth, P. Heath and R. Piccinini, Characterizing universal fibrations, Lecture notes in Math. 673 (Springer-Verlag, Berlin 1978) 168–184.

    MATH  Google Scholar 

  7. P. Booth, P. Heath, C. Morgan, and R. Piccinini, H-spaces of self-equivalences of fibrations and bundles, Proc. Lond. Math. Soc. (3) 49 (1984) 111–127.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Borel, Topics in the homology theory of fibre bundles, Lecture notes in Math. 36, Springer-Verlag, Berlin 1967.

    MATH  Google Scholar 

  9. A. Dold, Partitions of unity in the theory of fibrations, Ann. of Math. 78 (1963) 223–255.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Dror, W.G. Dwyer and D.M. Kan, Equivariant maps which are self-homotopy equivalences, Proc. Amer. Math. Soc. 80 (1980) 670–672.

    Article  MathSciNet  MATH  Google Scholar 

  11. W.G. Dwyer and D.M. Kan, Reducing equivariant homotopy theory to the theory of fibrations, Contemporary Mathematics, Vol 37 (1985) 35–49.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Fuchs, Borel fibrations and G-spaces, Manuscripta Math. 58 (1987) 377–380.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Fuchs, Equivariant maps up to homotopy and Borel spaces. Pub. Math. Univ. Aut. de Barcelona (1984) 79–102.

    Google Scholar 

  14. I.M. James, Ex-homotopy theory, Illinois J. Math. 15 (1971), 324–337.

    MathSciNet  MATH  Google Scholar 

  15. I.M. James, Alternative homotopy theories, L'Enseignement Mathématique, XXIII, fasc. 3–4 (1977) 221–237.

    MathSciNet  MATH  Google Scholar 

  16. D. Kahn, Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963) 432–450.

    MathSciNet  MATH  Google Scholar 

  17. P.J. Kahn, Some function spaces of CW-type Proc. Amer. Math. Soc. 90 (1984) 599–607.

    Article  MathSciNet  MATH  Google Scholar 

  18. S. MacLane, Categories for the working mathematician. Berlin: Springer-Verlag, Berlin, 1971.

    MATH  Google Scholar 

  19. J.P. May, Classifying spaces and fibrations, Memoirs Amer. Math. Soc. 155 (1975).

    Google Scholar 

  20. J. Milnor, Construction of universal bundles II, Ann. of Math. 63 (1956) 430–436.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Milnor, On spaces having the homotopy type of a CW-complex. Trans. Amer. Math. Soc. 90 (1959) 272–280.

    MathSciNet  MATH  Google Scholar 

  22. H. Oshima and K. Tsukiyama, On the group of equivariant self equivalences of free actions, Publ. RIMS, Kyoto Univ. 22 (1986) 905–923.

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Schön, Fibrations over a CWh-base, Proc. Amer. Math. Soc. 62 (1977) 165–166.

    Article  MathSciNet  MATH  Google Scholar 

  24. R. Schwaenzl and R.M. Vogt, Coherence in homotopy group actions, Transformation groups, Lecture notes in Math. 1217 (Springer-Verlag, Berlin, 1986) 364–390.

    Google Scholar 

  25. W. Shih, On the group ɛ[X] of homotopy equivalence maps. Bull. Amer. Math. Soc. 70 (1964) 361–365.

    Article  MathSciNet  MATH  Google Scholar 

  26. E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.

    MATH  Google Scholar 

  27. N. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967) 133–152.

    Article  MathSciNet  MATH  Google Scholar 

  28. R. Thom, L'homologie des espaces fonctionnels, Colloque. de Topologie Algébrique, Louvain (1956).

    Google Scholar 

  29. K. Tsukiyama, Equivariant self equivalences of principal fibre bundles, Proc. Camb. Phil. Soc. 98 (1985) 87–92.

    Article  MathSciNet  MATH  Google Scholar 

  30. K. Varadarajan, On fibrations and category, Math. Zeitschr. 88 (1965) 267–273.

    Article  MathSciNet  MATH  Google Scholar 

  31. R.M. Vogt, Convenient categories of topological spaces for homotopy theory, Arch. Math. 22 (1971) 545–555.

    Article  MathSciNet  MATH  Google Scholar 

  32. G.W. Whitehead, Elements of homotopy theory, Springer-Verlag, Berlin-Heidelberg-New York, (1978).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Memorial University of Newfoundland, A1C 5S7, St. John's, Canada

    Peter Booth

Authors
  1. Peter Booth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Renzo A. Piccinini

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Booth, P. (1990). Equivalent homotopy theories and groups of self-equivalences. In: Piccinini, R.A. (eds) Groups of Self-Equivalences and Related Topics. Lecture Notes in Mathematics, vol 1425. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083826

Download citation

  • DOI: https://doi.org/10.1007/BFb0083826

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52658-2

  • Online ISBN: 978-3-540-47091-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation