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Linearity of dimension functions for semilinear  -spheres
Author:
Ikumitsu Nagasaki
Journal:
Proc. Amer. Math. Soc. 130 (2002), 1843-1850
MSC (2000):
Primary 57S25; Secondary 57S15, 57S17
Posted:
January 25, 2002
MathSciNet review:
1887033
Full-text PDF Free Access
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Additional Information
Abstract: In this paper, we show that the dimension function of every semilinear  -sphere is equal to that of a linear  -sphere for finite nilpotent groups  of order  , where  ,  are primes. We also show that there exists a semilinear  -sphere whose dimension function is not virtually linear for an arbitrary nonsolvable compact Lie group  .
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- -, Homotopiedarstellungen endlich Gruppen: Dimensionsfunktionen, Invent. Math. 67 (1982), 231-252. MR 84b:57029
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- -, Transformation groups, Walter de Gruyter, Berlin, New York, 1987. MR 89c:57048
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- T. tom Dieck and T. Petrie, Homotopy representations of finite groups, Inst. Hautes Etudes Sci. Publ. Math. 56 (1982), 129-169. MR 86b:57020
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 , Mem. Amer. Math. Soc. 159 (1975). MR 51:6808
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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
Posted:
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
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