Quadratic-linear duality and rational homotopy theory of chordal arrangements

Bibby, Christin¹ ; Hilburn, Justin²

¹Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada
²Department of Mathematics, University of Oregon, 1380 Lawrence #2, Eugene, OR 97403, United States

Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2637-2661

Résumé

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 = ℂ), there is considerable literature on the rational homotopy theory of X, and the trigonometric case (C = 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).

Détail

DOI : 10.2140/agt.2016.16.2637

Classification : 16S37, 52C35, 55P62
Keywords: hyperplane arrangement, toric arrangement, elliptic arrangement, Koszul duality, rational homotopy theory

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