HOMOTOPY FIXED POINT SETS AND ACTIONS ON HOMOGENEOUS SPACES OF p-COMPACT GROUPS

Title & Authors
HOMOTOPY FIXED POINT SETS AND ACTIONS ON HOMOGENEOUS SPACES OF p-COMPACT GROUPS
Kenshi Ishiguro; Lee, Hyang-Sook;

Abstract
We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.
Keywords
p-compact groups;homotopy fixed point sets;fixed point sets;actions on homogeneous spaces;
Language
English
Cited by
References
1.
J. F. Adams and Z. Mahmud, Maps between classifying spaces, Invent. Math. 35 (1976), 1–41.

2.
J. F. Adams and C. W. Wilkerson, Finite H–spaces and algebras over the Steenrod algebra, Ann. of Math. 111 (1980), 95–143.

3.
A. Bousfield and D. Kan, Homotopy limits, completions and localizations, SLNM 304 (1972).

4.
C. Broto and S. Zarati, Nil-localization of unstable algebras over the Steenrod algebra, Math. Z. 199 (1988), 525–537.

5.
C. Broto and S. Zarati, On sub–\$A{^{\ast}_p}\$–algebras of \$H^{\ast}\$V , Proc. of 1990 Barcelona Conf., SLNM 1509 (1992), 35–49.

6.
E. Dror Farjoun and A. Zabrodsky, Fixed points and homotopy fixed points, Comment. Math. Helv. 63 (2) (1988), 286–295.

7.
W. G. Dwyer and C. W. Wilkerson, Smith theory and the functor T, Comment. Math. Helv. 66 (1) (1991), 1–17.

8.
W. G. Dwyer and C. W. Wilkerson, Homotopy fixed–point methods for Lie groups and finite loop spaces, Ann. of Math. 139 (2) (1994), 395–442.

9.
W. G. Dwyer and C. W. Wilkerson, The center of a p–compact group, The Čech centennial (Boston, MA, 1993), Contemp. Math. 181 (1995), 119–157.

10.
W. G. Dwyer, H. R. Miller and C. W. Wilkerson, Homotopical uniqueness of classifying spaces, Topology 31 (1) (1992), 29–45.

11.
W. G. Dwyer and A. Zabrodsky, Maps between classifying spaces, Proc. of 1986 Barcelona conference, LNM 1298 (1987), 106–119.

12.
D. Gorenstein, Finite groups, second edition, Chelsce (1980).

13.
W.-Y. Hsiang, Cohomology theory of topological transformation groups, Springer-Verlag, New York-Heidelberg (1975).

14.
K. Ishiguro, Classifying spaces and homotopy sets of axes of pairings, Proc. Amer. Math. Soc. 124 (1996), 3897–3903.

15.
K. Ishiguro, Toral groups and classifying spaces of p–compact groups, Contemp. Math. 271 (2001), 155–167.

16.
K. Ishiguro, Classifying spaces and a subgroup of the exceptional Lie group \$G_2\$, Contemp. Math. 274 (2001), 183–193.

17.
S. Jackowski, A fixed-point theorem for p-group actions, Proc. Amer. Math. Soc. 102 (1988), 205–208.

18.
J. Lannes, Sur la cohomologie modulo p des p–groupes Abeliens elementaires, Homotopy Theory, Proc. Durham Symp. 1985, Cambridge Univ. Press (1987), 97–116.

19.
H.-S. Lee, Homotopy fixed point set for p–compact toral group, Bull. Korean Math. Soc. 38 (2001), no. 1, 143–148.

20.
H. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), no. 2, 39–87.

21.
H. Miller, The Sullivan conjecture and homotopical representation theory, Proceedings of the ICM (Berkeley, Calif., 1986) (1987), 580–589.

22.
J. Moller and D. Notbohm, Centers and finite coverings of finite loop spaces, J. Reine Angew. Math. 456 (1994), 99–133.

23.
D. Notbohm, Spaces with polynomial mod–p cohomology, Math. Proc. Cambridge Philos. Soc. 126 (1999), no. 2, 277–292.

24.
D. Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. 94 (2) (1971), 549–572, 573–602.

25.
D. Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. 94 (2) (1971), 549–572, 573–602.