Abstract
Let $G$ be a finite group. Let $U_1,U_2,\dots$ be a sequence of orthogonal representations in which any irreducible representation of $\oplus_{n \geq 1} U_n$ has infinite multiplicity. Let $V_n=\oplus_{i=1}^n U_n$ and $S(V_n)$ denote the linear sphere of unit vectors. Then for any $i \geq 0$ the sequence of group $\dots \rightarrow \pi_i \operatorname{map}^G(S(V_n),S(V_n)) \rightarrow \pi_i \operatorname{map}^G(S(V_{n+1}),S(V_{n+1})) \rightarrow \dots$ stabilizes with the stable group $\oplus_H \omega_i(BW_GH)$ where $H$ runs through representatives of the conjugacy classes of all the isotropy group of the points of $S(\oplus_n U_n)$.
Original language | English |
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Publisher | ArXiv |
Publication status | Submitted - 29 Mar 2019 |
Keywords
- math.AT
- 55P91, 55Q52, 55P42