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||Abstract:||
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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