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The homotopy type of rational functions

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References

  1. Boyer, C.P., Mann, B.M.: Monopoles, non-linear σ-models, and two-fold loop spaces. Commun. Math. Phys.115, 571–594 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Brown, E.H., Peterson, F.P.: On the stable decomposition of Ω2 S r+2. Trans. Am. Math. Soc.243, 287–298 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cohen, F.R., Cohen, R.L., Mann, B.M., Milgram, R.J.: The topology of rational functions and divisors of surfaces. Acta Math.166(3), 163–221 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cohen, F.R., Mahowald, M., Milgram, R.J.: The stable decomposition of the double loop space of a sphere. In: Milgram, R.J. (ed.) Algebraic and Geometric Topology. (Proc. Symp. Pure Math., vol. 32, part 2, pp. 225–228) Providence, RI: Am. Math. Soc. 1978

    Google Scholar 

  5. Cohen, F.R., Taylor, L.R., May, J.P.: Splitting of certain spacesC(X). Math. Proc. Camb. Philos. Soc.84, 465–496 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cohen, R.L.: Stable proofs of stable splittings. Math. Proc. Camb. Philos. Soc.88, 149–151 (1980)

    Article  MATH  Google Scholar 

  7. Dold, A., Thom, R.: Quasifaserungen und unendliche symmetrische Produkte. Ann. Math.67, 239–281 (1958)

    Article  MathSciNet  Google Scholar 

  8. Kahn, D.S.: On the stable decomposition of Ω∞ S ∞ A. In: Barratt, M.G., Mahowald, M.E. (eds) Geometric Applications of Homotopy Theory II. (Lect. Notes Math., vol. 658, pp. 206–214) Berlin Heidelberg New York: Springer 1978

    Chapter  Google Scholar 

  9. Kahn, D.S., Priddy, S.: Applications of the transfer to stable homotopy theory. Bull. Am. Math. Soc.78, 981–987 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  10. May, J.P.: The Geometry of Iterated Loop Spaces. (Lect. Notes Math., vol. 271). Berlin Heidelberg New York: Springer 1972

    MATH  Google Scholar 

  11. Milgram, R.J.: Iterated loop spaces. Ann. Math.84, 386–403 (1966)

    Article  MathSciNet  Google Scholar 

  12. Segal, G.B.: The topology of rational functions. Acta Math.143, 39–72 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  13. Smith, L.: Transfer and ramified coverings. Math. Proc. Camb. Philos. Soc.93, 485–493 (1983)

    Article  MATH  Google Scholar 

  14. Snaith, V.P.: A stable decomposition of Ωn ∑n X. J. Lond. Math. Soc., II. Ser.7, 577–583 (1974)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Rochester, 14620, Rochester, NY, USA

    F. R. Cohen

  2. Department of Mathematics, Stanford University, Stanford, California, USA

    R. L. Cohen & R. J. Milgram

  3. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico

    B. M. Mann

Authors
  1. F. R. Cohen
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  2. R. L. Cohen
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  3. B. M. Mann
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  4. R. J. Milgram
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Additional information

During the preparation of this work each of the authors was supported by an NSF grant, the second author by an NSF-PYI award, and the first and fourth authors by the S.F.B. 170 in Göttingen

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Cohen, F.R., Cohen, R.L., Mann, B.M. et al. The homotopy type of rational functions. Math. Z. 213, 37–47 (1993). https://doi.org/10.1007/BF03025707

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