Algebraic & Geometric Topology

Torsion exponents in stable homotopy and the Hurewicz homomorphism

Akhil Mathew

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Abstract

We give estimates for the torsion in the Postnikov sections τ[1,n]S0 of the sphere spectrum, and we show that the p–localization is annihilated by pn(2p2)+O(1). This leads to explicit bounds on the exponents of the kernel and cokernel of the Hurewicz map π(X) H(X; ) for a connective spectrum X. Such bounds were first considered by Arlettaz, although our estimates are tighter, and we prove that they are the best possible up to a constant factor. As applications, we sharpen existing bounds on the orders of k–invariants in a connective spectrum, sharpen bounds on the unstable Hurewicz map of an infinite loop space, and prove an exponent theorem for the equivariant stable stems.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 2 (2016), 1025-1041.

Dates
Received: 26 March 2015
Revised: 29 July 2015
Accepted: 4 August 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841159

Digital Object Identifier
doi:10.2140/agt.2016.16.1025

Mathematical Reviews number (MathSciNet)
MR3493414

Zentralblatt MATH identifier
1353.55003

Subjects
Primary: 55P42: Stable homotopy theory, spectra 55Q10: Stable homotopy groups

Keywords
Adams spectral sequence vanishing lines Hurewicz homomorphism exponent theorems

Citation

Mathew, Akhil. Torsion exponents in stable homotopy and the Hurewicz homomorphism. Algebr. Geom. Topol. 16 (2016), no. 2, 1025--1041. doi:10.2140/agt.2016.16.1025. https://projecteuclid.org/euclid.agt/1510841159


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