Geometric fixed points of norms for positive-dimensional subgroups

About 4 years old · traced to

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 S⟶X\mathbb{S}\longrightarrow X induces a weak equivalence of derived geometric KK-fixed point spectra

(NeGX)ΦK≃S.(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.

References

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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.