## The four-color theorem and an instanton invariant for spatial graphs II

Tomasz Mrowka

Massachusetts Institute of Technology

October 13, 2015

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques from 3-dimensional topology: if the graph is bridgeless, its instanton homology is non-zero.