Authors: Jevtić, Filip 
Živaljević, Rade 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Generalized tonnetz and discrete abel-jacobi map
Journal: Topological Methods in Nonlinear Analysis
Volume: 57
Issue: 2
First page: 547
Last page: 567
Issue Date: 1-Jun-2021
Rank: ~M22
ISSN: 1230-3429
DOI: 10.12775/TMNA.2020.049
Motivated by classical Euler’s Tonnetz, we introduce and study the combinatorics and topology of more general simplicial complexes Tonnn k (L) of Tonnetz type. Out main result is that for a sufficiently generic choice of parameters the generalized Tonnetz Tonnn,k (L) is a triangulation of a (k-1)-dimensional torus Tk-1. In the proof we construct and use the properties of a discrete Abel-Jacobi map, which takes values in the torus Tk-1=ℝk-1/Λ where Λ=A*k-1 is the permutohedral lattice.
Keywords: Discrete Abel-Jacobi map | Generalized Tonnetz | Permutohedral lattice | Polyhedral combinatorics | Simplicial complexes | Triangulated manifolds
Publisher: Juliusz Schauder Center for Nonlinear Analysis

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