Not all free arrangements are $K(\pi,1)$

Paul H. Edelman; Victor Reiner

Not all free arrangements are $K(\pi,1)$

Algebraic Topology 2008-02-03 v1 Combinatorics

Authors: Paul H. Edelman , Victor Reiner

Abstract

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is $K(\pi,1)$ . These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well.

Keywords

hyperplane arrangements free arrangements k(pi,1) saito conjecture central symmetry octagon tilings

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@article{arxiv.math/9501229,
  title  = {Not all free arrangements are $K(\pi,1)$},
  author = {Paul H. Edelman and Victor Reiner},
  journal= {arXiv preprint arXiv:math/9501229},
  year   = {2008}
}

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5 pages

Not all free arrangements are $K(\pi,1)$

Abstract

Keywords

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