I am having trouble visualizing when a 2 form is exact and have a specific case that I am struggling with at the moment. Any help is welcome. Take an oriented 2 torus and divide it ,using parallel circles, into an even number of tube shaped regions. In each tube, assign a 2-form that fades to zero at its bounding circles and require the following: - these two forms fit together along the tube boundaries to give a global 2 form - Each form has the opposite orientation from the 2 forms in its adjacent regions - The integral of the induced global 2 form is zero. - None of the forms are identically zero in any tube. This form is exact. But how do I picture the one form that it is the exterior derivative of?