Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 8

Homological mirror symmetry of $\mathbb{F}_1$ via Morse homotopy

Pages: 2611 – 2637

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n8.a5

Authors

Masahiro Futaki (Department of Mathematics and Informatics, Graduate School of Science, Chiba University, Chiba, Japan)

Hiroshige Kajiura (Department of Mathematics and Informatics, Graduate School of Science, Chiba University, Chiba, Japan)

Abstract

This is a sequel to our paper $\href{https://doi.org/10.1063/5.0029165}{11}$, where we proposed a definition of the Morse homotopy of the moment polytope of toric manifolds. Using this as the substitute of the Fukaya category, we proved a version of homological mirror symmetry for the projective spaces and their products via Strominger–Yau–Zaslow construction of the mirror dual Landau–Ginzburg model.

In this paper we go this way further and extend our previous result to the case of the Hirzebruch surface $\mathbb{F}_1$.

Published 5 January 2024