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2016 Quadratic-linear duality and rational homotopy theory of chordal arrangements
Christin Bibby, Justin Hilburn
Algebr. Geom. Topol. 16(5): 2637-2661 (2016). DOI: 10.2140/agt.2016.16.2637


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).


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Christin Bibby. Justin Hilburn. "Quadratic-linear duality and rational homotopy theory of chordal arrangements." Algebr. Geom. Topol. 16 (5) 2637 - 2661, 2016.


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

zbMATH: 1373.55017
MathSciNet: MR3572342
Digital Object Identifier: 10.2140/agt.2016.16.2637

Primary: 16S37, 52C35, 55P62

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 5 • 2016
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