The RO(K)-graded homotopy of Klein-four normed Mackey functors

2025/07/16 by Bertrand Guillou, Guillou, Bertrand J., J. J. Keyes +3
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2507.12423

openalex publication_date 2025/07/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We compute the RO(K)-graded coefficients of the equivariant Eilenberg-Mac Lane spectrum associated to various Hill-Hopkins-Ravenel norms of the constant-\mathbbF₂ Mackey functor, where K is the Klein-four group. Further, we analyze the multiplicative structure of these RO(K)-graded Tambara functors.

Citations

• Representation-graded Bredon homology of elementary abelian 2-groups
• On the RO(Q)-graded coefficients of Eilenberg-MacLane spectra
• The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture
• The slice spectral sequence of a C₄-equivariant height-4 Lubin-Tate theory
• On the Andre-Quillen homology of Tambara functors
• An Equivariant Tensor Product on Mackey Functors
• Symmetric Powers and Norms of Mackey Functors
• The Equivariant Slice Filtration: a Primer
• Ideals of Tambara functors
• On the non-existence of elements of Kervaire invariant one
• On the nonexistence of elements of Kervaire invariant one
• An Atiyah-Hirzebruch spectral sequence for KR-theory

Related

• The RO(K)-graded Coefficients of H\underlineA
• On the RO(Q)-graded coefficients of Eilenberg-MacLane spectra
• On the structure of the RO(G)-graded homotopy of H\underlineM for cyclic p-groups
• On the RO(G)-graded coefficients of Q₈ equivariant cohomology
• Equivariant Eilenberg-Mac Lane spectra in cyclic p-groups