Algebraic & Geometric Topology

Quadratic-linear duality and rational homotopy theory of chordal arrangements

Christin Bibby and Justin Hilburn

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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 = ), 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).

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

Subjects
Primary: 16S37: Quadratic and Koszul algebras 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 55P62: Rational homotopy theory

Keywords
hyperplane arrangement toric arrangement elliptic arrangement Koszul duality rational homotopy theory

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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