The lower central series of a fiber-type arrangement

Michael J Falk, Richard Randell

Research output: Contribution to journalArticle

101 Citations (Scopus)

Abstract

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 examples Al. We also show that the formula does not hold for all K(π, 1) arrangements.

Original languageEnglish (US)
Pages (from-to)77-88
Number of pages12
JournalInventiones Mathematicae
Volume82
Issue number1
DOIs
StatePublished - Feb 1985
Externally publishedYes

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Lower Central Series
Arrangement
Fiber
Fundamental Group
Quotient
Complement
Polynomial

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The lower central series of a fiber-type arrangement. / Falk, Michael J; Randell, Richard.

In: Inventiones Mathematicae, Vol. 82, No. 1, 02.1985, p. 77-88.

Research output: Contribution to journalArticle

Falk, Michael J ; Randell, Richard. / The lower central series of a fiber-type arrangement. In: Inventiones Mathematicae. 1985 ; Vol. 82, No. 1. pp. 77-88.
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