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arXiv · 2112.14622

Equivariant Homological Mirror Symmetry for $\mathbb{C}$ and $\mathbb{C} P^1$

Masahiro Futaki·Fumihiko Sanda
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Abstract

In this paper we define an equivariant Floer $A_\infty$ algebra for $\mathbb{C}$ and $\mathbb{C} P^1$ by using Cartan model. We then prove an equivariant homological mirror symmetry, i.e. an equivalence between an $A_\infty$ category of equivariant Lagrangian branes and the category of matrix factorizations of Givental's equivariant Landau-Ginzburg potential function.

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Masahiro Futaki, Fumihiko Sanda. 2021-12-29. Equivariant Homological Mirror Symmetry for $\mathbb{C}$ and $\mathbb{C} P^1$. https://doi.org/10.1016/j.geomphys.2023.104929

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