Topological 5d $\mathcal{N}=2$ Gauge Theory: Novel Floer Homologies, their Dualities, and an $A_{\infty }$-category of Three-Manifolds

Arif Er, Zhi-Cong Ong, Meng-Chwan Tan

We show how one can define novel gauge-theoretic Floer homologies of four, three, and two-manifolds from the physics of a certain topologically-twisted 5d $\mathcal{N}=2$ gauge theory…