Classifying spaces and homotopy

sets of axes of pairings

Author:
Kenshi Ishiguro

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3897-3903

MSC (1991):
Primary 55R35; Secondary 55P15, 55P60

DOI:
https://doi.org/10.1090/S0002-9939-96-03497-1

MathSciNet review:
1343701

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Abstract | References | Similar Articles | Additional Information

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

**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*, 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 -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**

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Additional Information

**Kenshi Ishiguro**

Affiliation:
Department of Mathematics, Fukuoka University, Fukuoka 814-80, Japan

DOI:
https://doi.org/10.1090/S0002-9939-96-03497-1

Keywords:
Classifying space,
mapping spaces,
$p$-completion,
Lie groups,
weak epimorphism,
pairing

Received by editor(s):
April 10, 1995

Received by editor(s) in revised form:
June 15, 1995

Dedicated:
Dedicated to Professor Teiichi Kobayashi on his 60th birthday

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1996
American Mathematical Society