Braid group can be viewed as a symmetry group with a "one more dimension to pass through". Is there any "Galois theory", where the braid groups plays analoguos role as a symmetry groups in a native Galois theory? Can this be related to the purposes of lowdimensional topology?
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closed as unclear what you're asking by YCor, Stefan Kohl, Qiaochu Yuan, Ricardo Andrade, Theo JohnsonFreyd Mar 2 '14 at 2:14Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question. 

