Homotopy path algebras

• David Favero ^[1] ; Jesse Huang ^[2]
  1. [1] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  2. [2] University of Waterloo

     University of Waterloo

     Canadá

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01021-0
• Enlaces
  • Texto completo
• Resumen

  • We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and entrance/exit paths. As examples, we prove versions of homological mirror symmetry due to Bondal–Ruan for toric varieties and due to Berglund–Hübsch–Krawitz for hypersurfaces with maximal symmetry. We also demonstrate that a form of shellability implies Koszulity and the existence of a minimal cellular resolution. In particular, when the algebra determined by the image of the toric Frobenius morphism is directable, then it is Koszul and admits a minimal cellular resolution.

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