4manifolds and Arboricity

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=KzWecugE8fw

We realized this week that there is no upper bound on the arboricity of 3 or higher dimensional manifolds. We also have in general the lower bound d+1 for manifolds of dimension d. We start with these observations then look at some geometry of 4-manifolds like Gauss-Bonnet, Poincare-Hopf, Dehn-Sommerville, the Sard theorem and an index formula for the symmetric Poincare Hopf index involving codimension 2 manifolds. • Area footage was taken over the Cambridge Commons on Thursday, when it was still sunny. 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