Geometric fixed points of norms for positive-dimensional subgroups

From papers

Let GG be a compact Lie group, let K<GK<G be a closed subgroup of positive dimension, and let XX be a Dd\mathcal{D}^{d}-algebra whose underlying orthogonal spectrum is cofibrant, or a cofibrant commutative ring orthogonal spectrum. Positive-dimensional geometric fixed-point conjecture. The inclusion of the unit SX\mathbb{S}\longrightarrow X induces a weak equivalence of derived geometric KK-fixed point spectra

(NeGX)ΦKS.(N_e^G X)^{\Phi K}\simeq \mathbb{S}.

This predicts that norms from the trivial subgroup have only the sphere as geometric fixed points for positive-dimensional subgroups under the stated cofibrancy hypotheses.

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Primary source

Andrew J. Blumberg, Michael A. Hill and Michael A. Mandell, “Norms for compact Lie groups in equivariant stable homotopy theory”, arXiv:2212.11404 (2022).

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