Algebraic & Geometric Topology

Quadratic-linear duality and rational homotopy theory of chordal arrangements

Christin Bibby and Justin Hilburn

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To any graph and smooth algebraic curve C, one may associate a “hypercurve” arrangement, and one can study the rational homotopy theory of the complement X. In the rational case (C = ), there is considerable literature on the rational homotopy theory of X, and the trigonometric case (C = ×) is similar in flavor. The case when C is a smooth projective curve of positive genus is more complicated due to the lack of formality of the complement. When the graph is chordal, we use quadratic-linear duality to compute the Malcev Lie algebra and the minimal model of X, and we prove that X is rationally K(π,1).

Article information

Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2637-2661.

Received: 17 October 2014
Revised: 21 July 2015
Accepted: 29 January 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16S37: Quadratic and Koszul algebras 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 55P62: Rational homotopy theory

hyperplane arrangement toric arrangement elliptic arrangement Koszul duality rational homotopy theory


Bibby, Christin; Hilburn, Justin. Quadratic-linear duality and rational homotopy theory of chordal arrangements. Algebr. Geom. Topol. 16 (2016), no. 5, 2637--2661. doi:10.2140/agt.2016.16.2637.

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