Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 5 (2016), 2637-2661.
Quadratic-linear duality and rational homotopy theory of chordal arrangements
To any graph and smooth algebraic curve , one may associate a “hypercurve” arrangement, and one can study the rational homotopy theory of the complement . In the rational case (), there is considerable literature on the rational homotopy theory of , and the trigonometric case () is similar in flavor. The case when 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 , and we prove that is rationally .
Algebr. Geom. Topol., Volume 16, Number 5 (2016), 2637-2661.
Received: 17 October 2014
Revised: 21 July 2015
Accepted: 29 January 2016
First available in Project Euclid: 16 November 2017
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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