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Leibniz Rule on Higher Pages of Unstable Spectral Sequences

Part of: Spectral sequences Homotopy groups Applied homological algebra and category theory

Published online by Cambridge University Press:  01 February 2018

Sergei O. Ivanov ,
Roman Mikhailov  and
Jie Wu
Sergei O. Ivanov
Affiliation:
Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, St. Petersburg, 199178 Russia (ivanov.s.o.1986@gmail.com)
Roman Mikhailov
Affiliation:
Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, St. Petersburg, 199178 Russia (ivanov.s.o.1986@gmail.com) St. Petersburg Department of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023 Russia (rmikhailov@mail.ru)
Jie Wu*
Affiliation:
Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076 (matwuj@nus.edu.sg)
*
*Corresponding author.
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Abstract

A natural composition ⊙ on all pages of the lower central series spectral sequence for spheres is defined. Moreover, it is defined for the p-lower central series spectral sequence of a simplicial group. It is proved that the rth differential satisfies a ‘Leibniz rule with suspension’: d r (a ⊙ σ b) = ±d r a ⊙ b + a ⊙ d r σ b, where σ is the suspension homomorphism.

Keywords

spectral sequenceLeibniz rulelower central serieshomotopy groups

MSC classification

Primary: 55T15: Adams spectral sequences
Secondary: 55Q40: Homotopy groups of spheres 55Q05: Homotopy groups, general; sets of homotopy classes 55U10: Simplicial sets and complexes

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 1 , February 2018 , pp. 265 - 282
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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