Linearity of dimension functions for semilinear $G$-spheres
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- by Ikumitsu Nagasaki
- Proc. Amer. Math. Soc. 130 (2002), 1843-1850
- DOI: https://doi.org/10.1090/S0002-9939-02-06512-7
- Published electronically: January 25, 2002
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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 $G$.References
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Bibliographic 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
- 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
- Communicated by: Ralph Cohen
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1843-1850
- MSC (2000): Primary 57S25; Secondary 57S15, 57S17
- DOI: https://doi.org/10.1090/S0002-9939-02-06512-7
- MathSciNet review: 1887033
Dedicated: Dedicated to the memory of Professor Katsuo Kawakubo