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- W2051201857 abstract "A semilinear G-sphere means a smooth closed G-manifold such that for every subgroup H, the H-fixed point set is a homotopy sphere or empty. We introduce the Grothendieck group Ve(G) for a certain family of semilinear G-spheres, where e is an idempotent represented by a quasilinear G-disk of the Burnside ring A(G). In this paper we investigate the structure of Ve(G) and show that Ve(G) is isomorphic to JO(G); the Grothendieck group for linear G-spheres. On the other hand, both Ve(G) and JO(G) are naturally regarded as subgroups of the homotopy representation group V∞(G). We also show that Ve(G) and JO(G) are different subgroups of V∞(G) when e≠1." @default.
- W2051201857 created "2016-06-24" @default.
- W2051201857 creator A5065515234 @default.
- W2051201857 date "2004-11-01" @default.
- W2051201857 modified "2023-09-26" @default.
- W2051201857 title "The Grothendieck group of spheres with semilinear actions for a compact Lie group" @default.
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- W2051201857 doi "https://doi.org/10.1016/j.topol.2004.07.004" @default.
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