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- W4297200816 abstract "We study how the combinatorial structure of the Salvetti complexes of the braid arrangements are related to homotopy theoretic properties of iterated loop spaces. We prove the skeletal filtrations on the Salvetti complexes of the braid arrangements give rise to the cobar-type Eilenberg-Moore spectral sequence converging to the homology of $Omega^2Sigma^2 X$. We also construct a new spectral sequence that computes the homology of $Omega^{ell}Sigma^{ell} X$ for $ell>2$ by using a higher order analogue of the Salvetti complex. The $E^1$-term of the spectral sequence is described in terms of the homology of $X$. The spectral sequence is different from known spectral sequences that compute the homology of iterated loop spaces, such as the Eilenberg-Moore spectral sequence and the spectral sequence studied by Ahearn and Kuhn." @default.
- W4297200816 created "2022-09-27" @default.
- W4297200816 creator A5047386458 @default.
- W4297200816 date "2006-02-05" @default.
- W4297200816 modified "2023-09-28" @default.
- W4297200816 title "The Salvetti Complex and the Little Cubes" @default.
- W4297200816 doi "https://doi.org/10.48550/arxiv.math/0602085" @default.
- W4297200816 hasPublicationYear "2006" @default.
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