Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Classifying spaces and homotopy sets of axes of pairings

Author(s): Kenshi Ishiguro
Journal: Proc. Amer. Math. Soc. 124 (1996), 3897-3903.
MSC (1991): Primary 55R35; Secondary 55P15, 55P60
MathSciNet review: 1343701
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We consider the maps between classifying spaces of the form $BK \times BL \rightarrow BG$ . The main theorem shows that if the restriction map on $BL$ is a weak epimorphism, then the restriction on $BK$ should factor through the classifying spaces of the center of the compact Lie group $G$ . An application implies that $BG$ is an H-space (Hopf space) if and only if $G$ is abelian.

References:

1.: J. Aguadé and L. Smith, On the mod p torus theorem of John Hubbuck, Math. Z. 191 (1986), 325-326. MR 87e:57044
2.: G. Dula and D. Gottlieb, Splitting off H-spaces and Conner-Raymond Splitting Theorem, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 37 (1990), 321-334. MR 91i:55018
3.: W.G. Dwyer and G. Mislin, On the homotopy type of the components of $map_{*}(BS^{3}, BS^{3})$ , Proc. 1986 Barcelona conference, LNM 1298 (1987), 82-89. MR 89e:55018
4.: W.G. Dwyer and C. Wilkerson, The center of a -compact group, Preprint.
5.: W.G. Dwyer and A. Zabrodsky, Maps between classifying spaces, Proc. 1986 Barcelona conference, LNM 1298 (1987), 106-119. MR 89b:55018
6.: Y. Hemmi, The projective plane of an -pairing, J.P.A.A. 75 (1991), 277-296. MR 92m:55011
7.: K. Ishiguro, A -local splitting of , Proc. of AMS 95(2) (1985), 307-311. MR 86m:55023
8.: K. Ishiguro and D. Notbohm, Fibrations of classifying spaces, Transaction of AMS 343(1) (1994), 391-415. MR 94h:55028
9.: S. Jackowski, J.E. McClure and B. Oliver, Homotopy classification of self-maps of via -actions Part I and Part II, Ann. of Math. 135 (1992), 183-226, 227-270. MR 93e:55019
10.: S. Jackowski, J.E. McClure and B. Oliver, Self homotopy equivalences of classifying spaces of compact connected Lie groups, Preprint.
11.: R. Lashof, P. May and G. Segal, Equivariant bundles with abelian structural group, Contemporary Math. 19 (1983), 167-176. MR 85b:55023
12.: J. Lin, A cohomological proof of the torus theorem, Math. Z. 190 (1985), 469-476. MR 87c:55009
13.: G. Mislin and J. Thévenaz, The $Z^{*}$ -Theorem for compact Lie groups, Math. Ann. 291 (1991), 103-111. MR 92i:22006
14.: D. Notbohm, Maps between classifying spaces, Math. Z. 207 (1991), 153-168. MR 92b:55017
15.: D. Notbohm, Maps between classifying spaces and apllications,, J.P.A.A. 89 (1993), 273-294. MR 95c:55019
16.: N. Oda, The homotopy set of the axes of pairings, Canad. J. Math. 42 (1990), 856-868. MR 91i:55019
17.: N. Oda, Localization of the homotopy set of the axes of pairings, Adams memorial symposium on algegraic topology volume 1, London Math. Soc. Lecture Notes 175, Cambridge Univ. Press (1992), 163-177. MR 93i:55014

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|