Holonomy Lie algebras and the LCS formula for subarrangements of A_n

Details Holonomy Lie algebras and the LCS formula for subarrangements of A_n Holonomy Lie algebras and the LCS formula for subarrangements of A_n

2009-01-02

arxiv.org/abs/0901.0256v3

International Mathematics Research Notices, 8 (2009) 1421-1432

Mathematics

Algebraic Topology

v1: 9 pages, 1 figure v2: references added v3: minor rephrasing

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Holonomy Lie algebras and the LCS formula for subarrangements of A_n does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Holonomy Lie algebras and the LCS formula for subarrangements of A_n, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holonomy Lie algebras and the LCS formula for subarrangements of A_n will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-380957