Homotopy Path Algebras

David Favero; Jesse Huang

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arXiv · 2205.03730

Homotopy Path Algebras

David Favero·Jesse Huang

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Abstract

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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BibTeX RIS

David Favero, Jesse Huang. 2024-12-13. Homotopy Path Algebras. https://arxiv.org/abs/2205.03730

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