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I want to have a brief history about the low-dimensional manifolds and geometric structures on manifolds specially on low-dimensional manifolds .where I can read about thus ?

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Here is an essay from Milnor: maths.ed.ac.uk/~aar/papers/milnhist.pdf It only goes back to the 50s, but I found it quite interesting. – Adam Saltz Apr 21 '13 at 4:15
    
Thanks a lot Saltz. – david Apr 21 '13 at 4:44
    
In the 1980's, people started using ideas from physics to study the topology of $3$- and $4$-manifolds. See the following article of Atiyah for the early history of mathematical gauge theory: web.math.princeton.edu/~lewallen/AtiyahFloer.pdf – Henry T. Horton Apr 21 '13 at 19:22

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