HOMOLOGY OF THE GAUGE GROUP OF EXCEPTIONAL LIE GROUP G2

Title & Authors
HOMOLOGY OF THE GAUGE GROUP OF EXCEPTIONAL LIE GROUP G2
Choi, Young-Gi;

Abstract
We study homology of the gauge group associated with the principal $\small{G_2}$ 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
exceptional Lie group $\small{G_2}$;gauge group;iterated loop space;Dyer-Lashof operation;Serre spectral sequence;
Language
English
Cited by
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

2.
R. Bott, A note on the Samelson product in the classical groups, Comment. Math. Helv. 34 (1960), 249-256

3.
W. Browder, On differential Hopf algebra, Trans. Am. Math. Soc. 107 (1963), 153-176

4.
Y. Choi, On the Bockstein lemma, Topology Appl. 106 (2000), no. 2, 217-224

5.
W. Browder, Homology of the classifying space of Sp(n) gauge groups, Israel J. Math. 151 (2006), 167-177

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

8.
R. Kane, On loop spaces without p torsion, Pacific J. Math. 60 (1975), no. 1, 189-201

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

10.
J. P. Lin, On the collapses of certain Eilenberg-Moore spectral sequence, Topology Appl. 132 (2003), no. 1, 29-35

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

12.
J. W. Milnor and J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264

13.
M. Mimura, The Homotopy groups of Lie groups of low rank, J. Math. Kyoto Univ. 6 (1967), 131-176

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