The Bracket in the Bar Spectral Sequence for a Finite-fold Loop Space
نویسنده
چکیده
When X is an associative H-space, the bar spectral sequence computes the homology of the delooping, H∗(BX). If X is an n-fold loop space for n ≥ 2 this is a spectral sequence of Hopf algebras. Using machinery by Sugawara and Clark, we show that the spectral sequence filtration respects the Browder bracket structure on H∗(BX), and so it is moreover a spectral sequence of Poisson algebras. Through the bracket on the spectral sequence, we establish a connection between the degree n − 1 bracket on H∗(X) and the degree n − 2 bracket on H∗(BX). This generalizes a result of Browder and puts it in a computation-ready context.
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