A comparison of spectral sequences computing unstable homotopy groups of $p$-complete, nilpotent spaces

Details A comparison of spectral sequences computing unstable homotopy groups of $p$-complete, nilpotent spaces A comparison of spectral sequences computing unstable homotopy groups of $p$-complete, nilpotent spaces

2009-09-25

arxiv.org/abs/0909.4597v2

Mathematics

Algebraic Topology

26 pages

Scientific paper

The focus of this paper is the comparison of two unstable homotopy spectral sequences-- the unstable mod p Adams spectral sequence that computes the unstable homotopy of a p-complete space, and the Goerss--Hopkins spectral sequence, which computes the unstable homotopy of the space of E-infinity maps between Hk-algebras, where k is the algebraic closure of the field with p elements and p is an odd prime. Using an adjunction between p-complete nilpotent spaces and a subset of Hk-algebras, this paper shows that the unit of this adjunction provides an isomorphism between these spectral sequences.

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