Hopf Constructions and Higher Projective Planes for Iterated Loop Spaces

DOI10.2307/2154807zbMath0851.55015OpenAlexW4254945362MaRDI QIDQ4846108

Nicholas J. Kuhn, Michael Slack, Frank Williams

Publication date: 24 November 1996

Full work available at URL: https://doi.org/10.2307/2154807

zbMATH Keywords

cohomology classesSteenrod squaresH-spaceDyer-Lashof operationsiterated loop spaceHopf constructionhigher projective planeshigher projective spaces

Mathematics Subject Classification ID

(H)-spaces and duals (55P45) Loop spaces (55P35) Infinite loop spaces (55P47) Hopf invariants (55Q25)

Related Items (5)

Loops of \(H\)-spaces with finitely generated cohomology rings ⋮ \(H\)-spaces as direct product factors of loop spaces. ⋮ Topological nonrealization results via the Goodwillie tower approach to iterated loopspace homology ⋮ On decompositions in homotopy theory ⋮ Split dual Dyer-Lashof operations

Cites Work

• On the non-existence of elements of Hopf invariant one
• On functional cup-products and the transgression operator
• Maps between iterated loop spaces
• Extended powers of spectra and a generalized Kahn-Priddy theorem
• Homology operations and loop spaces
• Two torsion and the loop space conjecture
• The projective plane of an \(H\)-pairing
• The homology of iterated loop spaces
• A spectral sequence for the homology of an infinite delooping
• The geometry of the James-Hopf maps
• Unstable homotopy from the stable point of view
• On the projective plane of an H-space
• Iterated loop spaces
• A convenient category of topological spaces
• On homotopy commutative H-spaces
• \(H\)-spaces from a homotopy point of view
• The geometry of iterated loop spaces
• Implications in Morava 𝐾-theory
• Splitting of certain spaces CX
• Some properties of Hopf-type constructions
• Infinite loop spaces with trivial Dyer-Lashof operations
• Cohomology operations in iterated loop spaces
• Homotopy-everything 𝐻-spaces
• The metastable homotopy of 𝑆ⁿ
• Homology of Iterated Loop Spaces

This page was built for publication: Hopf Constructions and Higher Projective Planes for Iterated Loop Spaces