Discrete models for the \(p\)-local homotopy theory of compact Lie groups and \(p\)-compact groups

DOI10.2140/gt.2007.11.315zbMath1135.55008OpenAlexW2158483385WikidataQ115231053 ScholiaQ115231053MaRDI QIDQ873945

Ran Levi, Carles Broto, Robert Oliver

Publication date: 21 March 2007

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

Full work available at URL: https://doi.org/10.2140/gt.2007.11.315

zbMATH Keywords

Sylow subgroup\(p\)-compact grouporbit categoryfusion systems\(p\)-toral group

Mathematics Subject Classification ID

Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Homology and cohomology of Lie groups (57T10) Homology of classifying spaces and characteristic classes in algebraic topology (55R40)

Related Items (31)

The topological nilpotence degree of a Noetherian unstable algebra ⋮ Centric linking systems of locally finite groups ⋮ A Krull–Remak–Schmidt theorem for fusion systems ⋮ Strongly closed subgroups of finite groups. ⋮ Automorphisms of \(p\)-local compact groups ⋮ Normalizers of chains of discrete \(p\)-toral subgroups in compact Lie groups ⋮ Extensions of linking systems with \(p\)-group kernel ⋮ Existence and uniqueness of linking systems: Chermak's proof via obstruction theory ⋮ Recognizing nullhomotopic maps into the classifying space of a Kac-Moody group ⋮ On stratification for spaces with noetherian mod p cohomology ⋮ Weights for \(\ell\)-local compact groups ⋮ Subgroup collections controlling the homotopy type of a \(p\)-local compact group ⋮ Vector bundles over classifying spaces of p‐local finite groups and Benson–Carlson duality ⋮ Local Gorenstein duality for cochains on spaces ⋮ Unstable Adams operations on \(p\)-local compact groups ⋮ Unstable Adams operations acting on \(p\)-local compact groups and fixed points ⋮ Control of fixed points over discrete \(p\)-toral groups, and existence and uniqueness of linking systems ⋮ Depth and detection for Noetherian unstable algebras ⋮ An algebraic model for finite loop spaces ⋮ Mini-workshop: Chromatic phenomena and duality in homotopy theory and representation theory. Abstracts from the mini-workshop held March 4--10, 2018 ⋮ Loop space homology of a small category ⋮ The rational cohomology of a 𝑝-local compact group ⋮ Unitary embeddings of finite loop spaces ⋮ The cellular structure of the classifying spaces of finite groups ⋮ Existence and uniqueness of classifying spaces for fusion systems over discretep-toral groups ⋮ A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver. ⋮ Reduced fusion systems over p-groups with abelian subgroup of index p: III ⋮ Fusion systems ⋮ Stratification and duality for homotopical groups ⋮ Homotopy idempotent functors on classifying spaces ⋮ Heilbronn characters

Cites Work

• Classifying spaces of Kač-Moody groups
• The Segal conjecture for compact Lie groups
• Homotopy classification of self-maps of \(BG\) via \(G\)-actions. II
• Homotopy decomposition of classifying spaces via elementary Abelian subgroups
• Homotopy classification of self-maps of \(BG\) via \(G\)-actions. I
• Modules of topological spaces, applications to homotopy limits and \(E_ \infty\) structures
• Homotopy fixed-point methods for Lie groups and finite loop spaces
• Homotopy equivalences of \(p\)-completed classifying spaces of finite groups
• Homology decompositions for \(p\)-compact groups
• Frobenius categories.
• Sylow intersections and fusion
• Homotopy limits, completions and localizations
• Centric Maps and Realization of Diagrams in the Homotopy Category
• Higher limits via steinberg representations
• The homotopy theory of fusion systems
• Homotopy Lie groups
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