An approach to the Four Color Theorem via Gauge Theory and Three Manifold Topology

Tomasz Mrowka
Massachusetts Institute of Technology

A few years ago Peter Kronheimer and I realized that some of the invariants of knots in three manifolds coming from gauge theory had a generalization to invariants of knotted trivalent graphs. One of these invariants plausibly can be used to attack the four color theorem. In this talk I will sketch in rather broad terms some of these ideas. These invariants connect the four color problem to an important line of work combining gauge theory and 3 dimensional topology.

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