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

Masahiro Futaki, Fumihiko Sanda

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 symmetr…