Inventiones mathematicae

, Volume 82, Issue 1, pp 77–88

The lower central series of a fiber-type arrangement

  • Michael Falk
  • Richard Randell

DOI: 10.1007/BF01394780

Cite this article as:
Falk, M. & Randell, R. Invent Math (1985) 82: 77. doi:10.1007/BF01394780


For a certain class (“fiber-type”) of arrangements, including the supersolvable ones of Jambu and Terao [3], we prove a formula relating the Poincaré polynomial of the complement with the ranks of successive quotients in the lower central series of the fundamental group. Such a formula was proved by Kohno [5] for the single family of examplesAl.

We also show that the formula doesnot hold for allK(π, 1) arrangements.

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Michael Falk
    • 1
  • Richard Randell
    • 1
  1. 1.Department of MathematicsThe University of IowaIowa CityUSA