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- W4297806009 abstract "If X is the complement of a hypersurface in P^n, then Kohno showed that the nilpotent completion of the fundamental group is isomorphic to the nilpotent completion of the holonomy Lie algebra of X. When X is the complement of a hyperplane arrangement A, the ranks phi_k of the lower central series quotients of the fundamental group of X are known for isolated examples, and for two special classes: if X is hypersolvable (in which case the quadratic closure of the cohomology ring is Koszul), or if the holonomy Lie algebra decomposes in degree three as a direct product of local components. In this paper, we use the holonomy Lie algebra to obtain a formula for phi_k when A is a subarrangement of A_n. This extends Kohno's result for braid arrangements, and provides an instance of an LCS formula for arrangements which are not decomposable or hypersolvable." @default.
- W4297806009 created "2022-10-01" @default.
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- W4297806009 date "2009-01-02" @default.
- W4297806009 modified "2023-09-25" @default.
- W4297806009 title "Holonomy Lie algebras and the LCS formula for subarrangements of A_n" @default.
- W4297806009 doi "https://doi.org/10.48550/arxiv.0901.0256" @default.
- W4297806009 hasPublicationYear "2009" @default.
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