Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

HOMOLOGY OF THE GAUGE GROUP OF EXCEPTIONAL LIE GROUP G2

  • Choi, Young-Gi (Department of Mathematics Education Seoul National University)
  • Published : 2008.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

We study homology of the gauge group associated with the principal $G_2$ bundle over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the aid of homology and cohomology operations.

Keywords

References

  1. M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308 (1982), 523-615 https://doi.org/10.1098/rsta.1983.0017
  2. R. Bott, A note on the Samelson product in the classical groups, Comment. Math. Helv. 34 (1960), 249-256 https://doi.org/10.1007/BF02565939
  3. W. Browder, On differential Hopf algebra, Trans. Am. Math. Soc. 107 (1963), 153-176 https://doi.org/10.2307/1993874
  4. Y. Choi, On the Bockstein lemma, Topology Appl. 106 (2000), no. 2, 217-224 https://doi.org/10.1016/S0166-8641(99)00083-8
  5. W. Browder, Homology of the classifying space of Sp(n) gauge groups, Israel J. Math. 151 (2006), 167-177 https://doi.org/10.1007/BF02777360
  6. F. R. Cohen, T. Lada, and J. P. May, The Homology of Iterated Loop Spaces, Lect. Notes. Math. Vol. 533, Springer, 1976
  7. M. C. Crabb and W. A. Sutherland, Counting homotopy types of gauge groups, Proc. London Math. Soc. 81 (2000), no. 3, 747-768 https://doi.org/10.1112/S0024611500012545
  8. R. Kane, On loop spaces without p torsion, Pacific J. Math. 60 (1975), no. 1, 189-201 https://doi.org/10.2140/pjm.1975.60.189
  9. A. Kono and S. Tsukuda, 4-manifolds X over BSU(2) and the corresponding homotopy types Map(X;BSU(2)), J. Pure Appl. Algebra 151 (2000), no. 3, 227-237 https://doi.org/10.1016/S0022-4049(99)00069-9
  10. J. P. Lin, On the collapses of certain Eilenberg-Moore spectral sequence, Topology Appl. 132 (2003), no. 1, 29-35 https://doi.org/10.1016/S0166-8641(02)00360-7
  11. G. Masbaum, On the cohomology of the classifying space of the gauge group over some 4-complexes, Bull. Soc. Math. France 119 (1991), no. 1, 1-31 https://doi.org/10.24033/bsmf.2156
  12. J. W. Milnor and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264 https://doi.org/10.2307/1970615
  13. M. Mimura, The Homotopy groups of Lie groups of low rank, J. Math. Kyoto Univ. 6 (1967), 131-176 https://doi.org/10.1215/kjm/1250524375
  14. M. Mimura, Homotopy theory of Lie groups, Handbook of algebraic topology edited by I. M. James, North-Holland (1995), 953-991
  15. H. Toda, Composition Methods in Homotopy Groups of Spheres, Annals of Mathematics Studies, No. 49, Princeton University Press, Princeton, N. J., 1962