Description

• Title:
  Generalized Tonnetz and discrete Abel-Jacobi map
• Creator:
  Jevtić, Filip D.;
  Živaljević, Rade T.
• Description:
  Motivated by classical Euler's {\em Tonnetz}, we introduce and study the combinatorics and topology of more general simplicial complexes Tonn$^{n,k}(L)$ of {\em Tonnetz type}. Out main result is that for a sufficiently generic choice of parameters the generalized tonnetz Tonn$^{n,k}(L)$ is a triangulation of a $(k-1)$-dimensional torus $T^{k-1}$. In the proof we construct and use the properties of a {\em discrete Abel-Jacobi map}, which takes values in the torus $T^{k-1} \cong \mathbb{R}^{k-1}/\Lambda$ where $\Lambda \cong \mathbb{A}^\ast_{k-1}$ is the permutohedral lattice.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.05.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 2 (June 2021); 547 - 567;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.049/29009 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.049/29010
• Subject:
  Generalized Tonnetz;
  discrete Abel-Jacobi map;
  permutohedral lattice;
  simplicial complexes;
  polyhedral combinatorics;
  triangulated manifolds;
  Primary;
  57Q15;
  52B20;
  Secondary;
  14H40;
  52B05;
  52B70;
  52C07
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.049
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other