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Algebraic EHP Sequences Revisited

Part of: Homotopy groups Homological algebra Spectral sequences Operations and obstructions

Published online by Cambridge University Press:  03 December 2018

Thế Cu’ò’ng Nguyễn
Thế Cu’ò’ng Nguyễn*
Affiliation:
Vietnam Institute for Advanced Study in Mathematics, 1 Dai Co Viet Street, Ha Noi, Vietnam (tdntcuong@gmail.com) and Hanoi University of Science, VNU, 334 Nguyen Trai Street, Hanoi, Vietnam
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Abstract

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The algebraic EHP sequences, algebraic analogues of the EHP sequences in homotopy theory, are important tools in algebraic topology. This note will outline two new proofs of the existence of the algebraic EHP sequences. The first proof is derived from the minimal injective resolution of the reduced singular cohomology of spheres, and the second one follows Bousfield's idea using the loop functor of unstable modules.

Keywords

EHP sequencehomotopy groups of spheresJames modelSteenrod algebraunstable modules

MSC classification

Primary: 55Q40: Homotopy groups of spheres 55T15: Adams spectral sequences 55S10: Steenrod algebra
Secondary: 18G10: Resolutions; derived functors
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 3 , August 2019 , pp. 625 - 640
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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