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I am trying Witten's paper but unable to re-produce the computations presented in the paper. I tried few things on internet but all these tutorials explicitly don't show the calculations and refer to Witten's paper again for detailed calculations. Any suggestions if there is some material I can look at?

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Witten's paper doesn't contain any detailed calculations either. And a number of things in that paper were only proved later by Taubes and others. – David Roberts Oct 25 '12 at 7:45
Hey David, thank you. So what do you suggest to understand this. – Vijay Nov 9 '12 at 7:51

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