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Extended dyer-lashof algebras and modular coinvariants

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Abstract

Given an increasing sequence of integersN=(0,n 1,n 2,...), a functorG N is constructed from the category

of based spaces of the homotopy type ofCW compleces and based maps to a subcategory

of

in analogy to May's approximation modelC. A family of homology operationsRN is associated toG N and its algebraic structure is described in terms of modular coinvariants of parabolic subgroups.

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References

  1. Araki, S. and Kudo, T.: Topology ofH n -spaces andH-squaring operations. Mem. Fac. Sci. Kyusyu University seriesA 10, 85–120 (1964)

    MathSciNet  Google Scholar 

  2. Barratt, M. and Priddy, S.: On the Homology of Non-Connected Monoids and Their Associated Groups. Comm. Math. Helvet.,47, 1–14 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  3. Browder, W.: Homology operations in iterated loop spaces. Ill. J. Math.,14, 347–357 (1960)

    MathSciNet  Google Scholar 

  4. Campbell, H.E.A.: Upper triangular invariants. Canadian Bulletin,28, 243–248 (1985)

    MATH  Google Scholar 

  5. Campbell, H.E.A. and McCleary, J.: Homology operations and invariant theory. In preparation

  6. Campbell, H.E.A., Kechagias, N.E., and McCleary, J.: Homology operations and parabolic subgroups forp=2. In preparation

  7. Cartan, H. and Eilenberg. S.: Homological Algebra. Princeton University Press, (1956)

  8. Cohen, F., Lada, T., and May, P.J.: The homology of iterated loop spaces. Lecture notes in Mathematics,533. (1975)

  9. Dickson, L.E.: A fundanental system of invariants of the general modular linear group with a solution of the form problem. Trans. Amer. Math. Soc.,12, 75–98, (1911)

    Article  MathSciNet  MATH  Google Scholar 

  10. Dyer, E. and Lashof, R.K.: Homology of iterated loop spaces. American Journal of Mathematics,84, 35–88, (1962)

    Article  MATH  MathSciNet  Google Scholar 

  11. Huynh Mui: Modular invariant theory and the cohomology algebras of the symmetric group. J. Fac. Sci., Univ. Tokyo,22, 319–369 (1975)

    MATH  MathSciNet  Google Scholar 

  12. Huynh Mui: Homology operations derived from modular coinvariants. Lecture Notes in Mathematics,172, 85–115, (1985)

    Google Scholar 

  13. Kechagias, N.E.: Ph. D. thesis. Queen's University, Kingston Ontario. (1990)

  14. Kechagias, N.E.: The Steenrod algebra action on generators of rings in invariants of subgroups ofGL(n, Z/pZ). Proc. Amer. Math. Soc.118, 943–952, (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Kechagias, N.E.: Homology operations, limit spaces, and modular coinvariants. Can. Jour. Math.45, 803–819, (1993)

    MATH  MathSciNet  Google Scholar 

  16. Kuhn, N.: Chevalley group theory and the transfer in the homology of symmetric groups. Topology121, 247–264, (1985)

    Article  MathSciNet  Google Scholar 

  17. Madsen, I.: On the action of Dyer-Lashof algebra inH*(B). Pacific Journal of Mathematics60, 235–275, (1975)

    MATH  MathSciNet  Google Scholar 

  18. Madsen, I. and Milgram, R.J.: The classifying spaces for surgery and cobordism of manifolds. Princeton University Press,92, (1979)

  19. May, P.J.: A general algebraic approch to Steenrod operations. Lecture notes in Mathematics168, 153–231, (1970)

    Article  MathSciNet  Google Scholar 

  20. May, P.J.: The geometry of Iterated loop spaces. L. N. M.971, (1973)

  21. Milgram, R.J.: Iterated loop spaces. Annals of Math.84, 386–403, (1966)

    Article  MathSciNet  Google Scholar 

  22. Milnor, J. and Moore, J.C.: On the structure of Hopf algebras. Annals of Math.81, 211–264, (1965)

    Article  MathSciNet  Google Scholar 

  23. Nakaoka, M.: Decomposition theorem for homology groups of symmetric groups. Annals of Mathematics71, 16–42, (1960)

    Article  MathSciNet  Google Scholar 

  24. Nakaoka, M.: Homology of the infinite symmetric group. Annals of Mathematics73, 229–257, (1961)

    Article  MathSciNet  Google Scholar 

  25. Nishida, G.: Cohomology operations in iterated loop spaces. Proc. Japan Acad.73, 104–109, (1968)

    Article  MathSciNet  Google Scholar 

  26. Priddy, S.: OnΩ ∞ S ∞ and the infinite symmetric group. Proc. Symp. Pure Math.22, 217–220, (1971)

    MathSciNet  Google Scholar 

  27. Steenrod, N. and Epstein, D.B.A.: Cohomology Operations. Princeton University Press,50, (1962)

  28. Wilkerson, C.W.: A primer on Dickson invariants. Cont. Math.19, 421–434, (1983)

    MATH  MathSciNet  Google Scholar 

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Author notes

  1. Nondas E. Kechagias

    Present address: Department of Mathematics, University of the Aegean, Karlovassi, 83200, Samos, Greece

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  1. Department of Mathematics and Statistics, York University, 4700 Keele Street, M3J 1P3, Canada

    Nondas E. Kechagias

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  1. Nondas E. Kechagias
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Kechagias, N.E. Extended dyer-lashof algebras and modular coinvariants. Manuscripta Math 84, 261–290 (1994). https://doi.org/10.1007/BF02567457

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  • DOI: https://doi.org/10.1007/BF02567457

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