Geometric fixed points of norms for positive-dimensional subgroups
Geometric fixed points of norms for positive-dimensional subgroups
Let be a compact Lie group, let be a closed subgroup of positive dimension, and let be a -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 induces a weak equivalence of derived geometric -fixed point spectra
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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