Abstract: The four color theorem was proved by Appel and Haken in 1989 using a computer. At ICM 2018, Kronheimer and Mrowka proposed an alternative way based on gauge theory in low-dimensional topology that might give a new proof of this theorem. This talk is a survey of their approach. First, I'll explain the relation between the SO(3) representation variety of a trivalent graph and the four color theorem. Then I'll review some properties of singular instanton Floer homology J^# of a trivalent graph.
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