## Algebraic & Geometric Topology

### Quadratic-linear duality and rational homotopy theory of chordal arrangements

#### 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 ($C = ℂ×$) 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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841222

Digital Object Identifier
doi:10.2140/agt.2016.16.2637

Mathematical Reviews number (MathSciNet)
MR3572342

Zentralblatt MATH identifier
1373.55017

#### Citation

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. https://projecteuclid.org/euclid.agt/1510841222

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