Abstract
Let G be a finite group. The Smith equivalence for real G-modules of finite dimension gives a subset of real representation ring, called the primary Smith set. Since the primary Smith set is not additively closed in general, it is an interesting problem to find a subset which is additively closed in the real representation ring and occupies a large portion of the primary Smith set. In this paper we introduce an additively closed subset of the primary Smith set by means of smooth one-fixed-point G-actions on spheres, and we give evidences that the subset occupies a large portion of the primary Smith set if G is an Oliver group.
| Original language | English |
|---|---|
| Pages (from-to) | 1003-1013 |
| Number of pages | 11 |
| Journal | Osaka Journal of Mathematics |
| Volume | 53 |
| Issue number | 4 |
| Publication status | Published - Oct 1 2016 |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
Cite this
One-fixed-point actions on spheres and smith sets. / Morimoto, Masaharu.
In: Osaka Journal of Mathematics, Vol. 53, No. 4, 01.10.2016, p. 1003-1013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - One-fixed-point actions on spheres and smith sets
AU - Morimoto, Masaharu
PY - 2016/10/1
Y1 - 2016/10/1
N2 - Let G be a finite group. The Smith equivalence for real G-modules of finite dimension gives a subset of real representation ring, called the primary Smith set. Since the primary Smith set is not additively closed in general, it is an interesting problem to find a subset which is additively closed in the real representation ring and occupies a large portion of the primary Smith set. In this paper we introduce an additively closed subset of the primary Smith set by means of smooth one-fixed-point G-actions on spheres, and we give evidences that the subset occupies a large portion of the primary Smith set if G is an Oliver group.
AB - Let G be a finite group. The Smith equivalence for real G-modules of finite dimension gives a subset of real representation ring, called the primary Smith set. Since the primary Smith set is not additively closed in general, it is an interesting problem to find a subset which is additively closed in the real representation ring and occupies a large portion of the primary Smith set. In this paper we introduce an additively closed subset of the primary Smith set by means of smooth one-fixed-point G-actions on spheres, and we give evidences that the subset occupies a large portion of the primary Smith set if G is an Oliver group.
UR - http://www.scopus.com/inward/record.url?scp=84990045957&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84990045957&partnerID=8YFLogxK
M3 - Article
VL - 53
SP - 1003
EP - 1013
JO - Osaka Journal of Mathematics
JF - Osaka Journal of Mathematics
SN - 0030-6126
IS - 4
ER -