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Homology of the classifying space ofSp(n) Gauge groups

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Abstract

We study the modp homology of the classifying space of the gauge group associated with the principalSp(n) bundle over the four-sphere using the Serre spectral sequence for the evaluation fibration.

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References

  1. S. Akbulut,On universal relations in gauge theory, Transactions of the American Mathematical Society348 (1996), 1329–1355.

    Article  MathSciNet  Google Scholar 

  2. M. F. Atiyah and R. Bott,The Yang-Mills equations over Riemann surfaces, Philosophical Transactions of the Royal Society of London, Series A308 (1982), 523–615.

    Article  MathSciNet  Google Scholar 

  3. R. Bott,The stable homotopy of the classical Lie groups, Annals of Mathematics70 (1959), 313–337.

    Article  MathSciNet  Google Scholar 

  4. R. Bott,A note on the Samelson product in the classical groups, Commentarii Mathematici Helvetici34 (1960), 249–256.

    Article  MathSciNet  Google Scholar 

  5. [5] Y. Choi,On the mod 2 homology of Sp(n) instantons and the classifying space of the gauge group, Bulletin of the Australian Mathematical Society55 (1997), 503–512.

    Article  MathSciNet  Google Scholar 

  6. Y. Choi and S. Yoon,Homology of the double and the triple loop spaces of E 6, E7, and E8, Manuscripta Mathematica103 (2000), 101–116.

    Article  MathSciNet  Google Scholar 

  7. F. R. Cohen, T. Lada and J. P. May,The homology of iterated loop spaces, Lecture Notes in Mathematics533, Springer, Berlin, 1976.

    MATH  Google Scholar 

  8. R. Kane,On loop spaces without p torsion, Pacific Journal of Mathematics60 (1975), 189–201.

    Article  MathSciNet  Google Scholar 

  9. A. Kono and S. Tsukuda,4-manifolds X over B SU(2)and the corresponding homotopy types Map(X, B SU(2)), Journal of Pure and Applied Algebra151 (2000), 227–237.

    Article  MathSciNet  Google Scholar 

  10. J. P. Lin,On the collapses of certain Eilenberg-Moore spectral sequence, Topology and its Applications132 (2003), 29–35.

    Article  MathSciNet  Google Scholar 

  11. G. Masbaum,On the cohomology of the classifying space of the gauge group over some 4-complexes, Bulletin de la Société Mathématique de France119 (1991), 1–31.

    Article  MathSciNet  Google Scholar 

  12. J.-P. Serre,Groupes d'homotopie et classes de groupes abeliens, Annals of Mathematics58 (1953), 258–294.

    Article  MathSciNet  Google Scholar 

  13. W. A. Sutherland,Function spaces related to gauge groups, Proceedings of the Royal Society of Edinburgh. Section A121 (1992), 185–190.

    Article  MathSciNet  Google Scholar 

  14. H. Toda,Composition methods in homotopy groups of spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N.J., 1962.

    MATH  Google Scholar 

  15. G. W. Whitehead,On products in homotopy groups, Annals of Mathematics47 (1946), 460–475.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics Education, Seoul National University, 151-748, Seoul, Korea

    Younggi Choi

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  1. Younggi Choi
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Additional information

This work was supported by Korea Research Foundation Grant KRF-2002-041-C00032.

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Choi, Y. Homology of the classifying space ofSp(n) Gauge groups. Isr. J. Math. 151, 167–177 (2006). https://doi.org/10.1007/BF02777360

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  • DOI: https://doi.org/10.1007/BF02777360

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