A differential algebra and the homotopy type of the complement of a toric arrangement

TL;DR

This paper demonstrates that the rational homotopy type of a toric arrangement's complement can be fully characterized by combinatorial data, using a differential graded algebra approach.

Contribution

It introduces a differential graded algebra whose minimal model captures the rational homotopy type of toric arrangement complements, linking algebraic and combinatorial structures.

Findings

Rational homotopy type determined by combinatorial data

Construction of a differential graded algebra model

Equivalence to Sullivan minimal model

Abstract

We show that the rational homotopy type of the complement of a toric arrangement is completely determined by two sets of combinatorial data. This is obtained by introducing a differential graded algebra over Q whose minimal model is equivalent to the Sullivan minimal model of the arrangement.