Modular representations of \(GL(n,p)\), splitting \(\Sigma(CP^{\infty} \times \dots \times CP^{\infty})\) and the \(\beta\)-family as framed hypersurfaces

DOI10.1007/BF01175047zbMath0536.55006MaRDI QIDQ791925

S. Hilditch, Lionel Schwartz, Peter J. Eccles, R. M. W. Wood, Grant Walker, Nigel Ray, David P. Carlisle

Publication date: 1985

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173579

zbMATH Keywords

localisationmodular representationstable homotopyprimitive idempotentbeta-family\(p\)-primary component of the stable homotopy groups of spheresdouble complex transferframed hypersurfacestable splittings of the classifying space of the \(n\)-torus

Mathematics Subject Classification ID

Modular representations and characters (20C20) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Stable homotopy theory, spectra (55P42) Other types of cobordism (57R90) Stable homotopy of spheres (55Q45)

Related Items (10)

On the detection of some elements in the image of the double transfer using K(2)-theory ⋮ Poincaré series for the occurrence of certain modular representations of GL(n,p) in the symmetric algebra ⋮ On the iterated complex transfer ⋮ Wilson spaces and stable splittings of BT^r ⋮ Quelques éléments dans l'homotopie stable du groupe unitaire ⋮ Truncated symmetric powers and modular representations of GL_n ⋮ A note on the double quaternionic transfer and its $f$–invariant ⋮ The transfer in homological algebra ⋮ The module structure of a group action on a polynomial ring ⋮ Splitting \(B({\mathbb{Z}}/p)^ n\) and \(BT^ n\) via modular representation theory

Cites Work

• Unnamed Item
• Unnamed Item
• Stable splittings derived from the Steinberg module
• Stable properties of rank 1 loop structures
• Lie groups as framed manifolds
• Splitting certain suspensions via self-maps
• Periodic phenomena in the Adams-Novikov spectral sequence
• A study of certain modular representations
• Mod p decomposition of compact Lie groups
• Mod p decompositions of co H-spaces and applications
• On the groups \(J(X)\). IV
• Embedding certain complexes up to homotopy type in euclidean space
• $p$-primary components of homotopy groups IV. Compositions and toric constructions
• On the Kummer Congruences and the Stable Homotopy of BU
• Some infinte families of U-hypersurfaces.
• Embedding certain complexes via unstable homotopy theory
• The Elements β₁ are Representable as Framed Hypersurfaces
• Opérations d'Adams en K-homologie et applications
• The order of the image of the 𝐽-homomorphism
• On Realizing Complex Bordism Modules: Applications to the Stable Homotopy of Spheres
• Applications of the transfer to stable homotopy theory

This page was built for publication: Modular representations of \(GL(n,p)\), splitting \(\Sigma(CP^{\infty} \times \dots \times CP^{\infty})\) and the \(\beta\)-family as framed hypersurfaces