Not all free arrangements are K(π, 1)

Paul H. Edelman; Victor Reiner

doi:10.1090/S0273-0979-1995-00557-4

Not all free arrangements are K(π, 1)

Paul H. Edelman, Victor Reiner

Mathematics

Research output: Contribution to journal › Comment/debate › peer-review

4 Scopus citations

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(π, 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.

Original language	English (US)
Pages (from-to)	61-65
Number of pages	5
Journal	Bulletin of the American Mathematical Society
Volume	32
Issue number	1
DOIs	https://doi.org/10.1090/S0273-0979-1995-00557-4
State	Published - Jan 1995

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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(π, 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.",

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AU - Reiner, Victor

PY - 1995/1

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AB - 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(π, 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.

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U2 - 10.1090/S0273-0979-1995-00557-4

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Not all free arrangements are K(π, 1)

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