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Abstract

Given any n points on a manifold, how can we systematically and continuously find a new point? What if we ask them to be distinct? In this thesis, I will try to answer these ques- tion on surfaces. Then I will connect these questions to sections of some universal surface bundles. In the end, I will classify automorphisms of n-strand surface braid group. The slogan is ”there is no center of mass on closed hyperbolic surfaces”.

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