Incomplete Tambara functors

DOI10.2140/agt.2018.18.723zbMath1388.55011arXiv1603.03292OpenAlexW3098270653WikidataQ130131888 ScholiaQ130131888MaRDI QIDQ1743502

Andrew J. Blumberg, Michael A. Hill

Publication date: 13 April 2018

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.03292

zbMATH Keywords

equivariant homotopyMackey functorTambara functor

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) Equivariant homology and cohomology in algebraic topology (55N91) Special categories (18B99) Frobenius induction, Burnside and representation rings (19A22) Equivariant homotopy theory in algebraic topology (55P91)

Related Items (19)

Global transfer systems of abelian compact Lie groups ⋮ The genuine operadic nerve ⋮ On the André-Quillen homology of Tambara functors ⋮ On distributivity in higher algebra I: the universal property of bispans ⋮ Global N∞$N_\infty$‐operads ⋮ Genuine‐commutative structure on rational equivariant K$K$‐theory for finite abelian groups ⋮ Bi-incomplete Tambara functors as \(\mathcal{O}\)-commutative monoids ⋮ \(G_\infty\)-ring spectra and Moore spectra for \(\beta\)-rings ⋮ Idempotent characters and equivariantly multiplicative splittings of K‐theory ⋮ Multiplicativity of the idempotent splittings of the Burnside ring and the \(G\)-sphere spectrum ⋮ Generalized \(\mathbb{Z}\)-homotopy fixed points of \(C_n\) spectra with applications to norms of \(MU_{\mathbb{R}}\) ⋮ Combinatorial \(N_\infty\) operads ⋮ The right adjoint to the equivariant operadic forgetful functor on incomplete Tambara functors ⋮ \(N_\infty \)-operads and associahedra ⋮ The Witt vectors for Green functors ⋮ \(G\)-symmetric monoidal categories of modules over equivariant commutative ring spectra ⋮ DETECTING STEINER AND LINEAR ISOMETRIES OPERADS ⋮ Equivariant stable categories for incomplete systems of transfers ⋮ The localized slice spectral sequence, norms of real bordism, and the Segal conjecture

Cites Work

• Spectral Mackey functors and equivariant algebraic \(K\)-theory. I.
• On the fractions of semi-Mackey and Tambara functors
• Ideals of Tambara functors
• Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads
• Operadic multiplications in equivariant spectra, norms, and transfers
• Localization and completion theorems for \(MU\)-module spectra
• On the nonexistence of elements of Kervaire invariant one
• On multiplicative transfer
• Polynomial functors and polynomial monads
• Polynomials in categories with pullbacks

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