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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linearity of dimension functions for semilinear $G$-spheres


Author: Ikumitsu Nagasaki
Journal: Proc. Amer. Math. Soc. 130 (2002), 1843-1850
MSC (2000): Primary 57S25; Secondary 57S15, 57S17
Published electronically: January 25, 2002
MathSciNet review: 1887033
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Abstract: In this paper, we show that the dimension function of every semilinear $G$-sphere is equal to that of a linear $G$-sphere for finite nilpotent groups $G$ of order $p^nq^m$, where $p$, $q$are primes. We also show that there exists a semilinear $G$-sphere whose dimension function is not virtually linear for an arbitrary nonsolvable compact Lie group $G$.


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Additional Information

Ikumitsu Nagasaki
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka 560-0043, Osaka, Japan
Email: nagasaki@math.sci.osaka-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06512-7
PII: S 0002-9939(02)06512-7
Keywords: Dimension function, semilinear $G$-sphere, homotopy representation
Received by editor(s): March 20, 2000
Published electronically: January 25, 2002
Additional Notes: This work was partially supported by Grant-in-Aid for Scientific Research
Dedicated: Dedicated to the memory of Professor Katsuo Kawakubo
Communicated by: Ralph Cohen
Article copyright: © Copyright 2002 American Mathematical Society