#### Title

Quadratic-linear duality and rational homotopy theory of chordal arrangements

#### Document Type

Article

#### Publication Date

11-7-2016

#### Abstract

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 D 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). x

#### Publication Source (Journal or Book title)

Algebraic and Geometric Topology

#### First Page

2637

#### Last Page

2661

#### Recommended Citation

Bibby, C., & Hilburn, J.
(2016). Quadratic-linear duality and rational homotopy theory of chordal arrangements.* Algebraic and Geometric Topology**, 16* (5), 2637-2661.
https://doi.org/10.2140/agt.2016.16.2637