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Generally the Poincaré conjecture is revolved around Topology, which deals with spaces. Apparently the Poincaré conjecture fixes up singularities in the dimensions e.t.c.

My question is, what are all the ramifications for the solution of the Poincaré conjecture, i.e. does it give proof or rise to new mathematics like quantum cohomology (Apparently, one of the other problems, call the Yang-mills existence and mass gap gives rise to Quantum cohomology, but Yang-mills theory has to have a mathematically rigorous background before quantum cohomology can be taken seriously)?

Also, What are the physical implication of the proof of Poincaré conjecture i.e. as i mentioned previously, this proof fixes the singularities in topology, so topologically speaking, what are the ramifications for blackholes and the big bang?

All you well educated opinions are well appreciated, as i am just a layman