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Quadratic-linear duality and rational homotopy theory of chordal arrangements

Christin Bibby and Justin Hilburn

Algebraic & Geometric Topology 16 (2016) 2637–2661

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).

hyperplane arrangement, toric arrangement, elliptic arrangement, Koszul duality, rational homotopy theory
Mathematical Subject Classification 2010
Primary: 16S37, 52C35, 55P62
Received: 17 October 2014
Revised: 21 July 2015
Accepted: 29 January 2016
Published: 7 November 2016
Christin Bibby
Department of Mathematics
University of Western Ontario
London, ON N6A 5B7
Justin Hilburn
Department of Mathematics
University of Oregon
1380 Lawrence #2
Eugene, OR 97403
United States