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user 22989
21
votes
Accepted
Do mutually dual finite vector spaces have the same orbit cardinalities under a linear group...
Yes. In particular, it can happen that $V$ has non-zero fixed points, but $V^*$ doesn't.
For example, let $G$ be the symmetric group of degree 3 acting in the obvious way on the set $\{e_1,e_2,e_3\}$ …
- 35.2k
5
votes
Free and cellular G-action implies free G-complex?
If $G$ acts freely on a CW-complex, permuting the cells, then the stabilizer of a cell must be finite (and therefore trivial, as pointed out in the question).
This can be shown by induction on the di …
- 35.2k