Thank you very much for such a clear exposition on gauge. I am a bachelor’s student, recently been trying to understand Donaldson and Kronheimer’s exposition The Geometry of Four Manifolds.

I have a somewhat naive question. I came across the following comment: ” Our ASD equation is non-linear, but more to the point it is not elliptic, i.e, the highest order part is not elliptic. This is clear from abstract grounds from the invariance of the equation under gauge transformations.”

How is the gauge group responsible for the ellipticity of the operator?

Varun

]]>Here’s a great answer from Terence Tao: http://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/

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