I was reading the textbook "Hodge Decomposition A Method for Solving Boundary Value Problems" by Günter Schwarz.
I wanted to find a simple example of the “hodge-morrey-friedrich decomposition”. I thought that a punctured 2-dimensional disk would be a good example, since it is related to de rham cohomology.
So My conclusion was that I could think 1-form $(xdx+ydy)/($x^2$+$y^2$)$ is ismomorphic to $H^1$$(M,δ)$
Is this example appropriate?
Since my major is not mathematics, there might be some mistakes in my questions. If you find any errors or issues, I would be very happy to hear from you. And of course, I would also be very happy to hear the answer to my question.