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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 18th 2019

    I have added the statement that GG-representation spheres are GG-CW-complexes, with a sketch of the idea of the proof for finite groups (here)

    I have been looking for source (be it textbook lecture note or otherwise) that makes this statement and gives a proof in a citable way. But it seems people either like to state it as an exercise or else spell it out only in special cases.

    diff, v13, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 10th 2020

    added remark on relation to projective GG-spaces:

    Similarly, if VV is 1-dimensional over the given ground field kk, stereographic projection identifies the representation sphere of VV with the projective G-space of V1V \oplus \mathbf{1}:

    V cpt kP(V1) v {[v,1] | vV [1,0] | v= \array{ V^{cpt} & \longrightarrow & k P \big( V \oplus \mathbf{1} \big) \\ v &\mapsto& \left\{ \array{ [v,1] &\vert& v \in V \\ [1,0] &\vert& v = \infty } \right. }

    diff, v19, current